Fh91 william fulton and joe harris, representation theory, graduate texts in mathematics, vol. Vera serganova then discussed some aspects of the representation theory of lie superalgebras. Since the center of the universal enveloping algebra uacts triviallyon all irreducible. The representation theory of the exceptional lie superalgebras f4 and g3 by lilit martirosyan a dissertation submitted in partial satisfaction of the requirements for the degree of doctor of philosophy in mathematics in the graduate division of the university of california, berkeley committee in charge. However it is somewhat out of date in that it uses the original atlas interface, rather than the newer realex interface. The institute is located at 17 gauss way, on the university of california, berkeley campus, close to grizzly peak, on the. Borelweilbott theory, associated variety and odd nilpotent cone. Fun applications of representations of finite groups. A journey through representation theory from finite.
Landmarks in representation theory caroline gruson and. The exposition will be heavily geometric, and connections to other areas of mathematics will be strongly emphasized, including, but not limited to, di. Vera serganova department of mathematics at university. Green correspondence and relative projectivity for pairs of adjoint functors between triangulated categories. Vera serganovas research works university of california. In his book cubic forms manin discovered that del pezzo surfaces are related to root systems. Retrieve articles in representation theory of the american mathematical society with msc 1991. A journey through representation theory from finite groups to. Vera serganova s 99 research works with 975 citations and 2,092 reads, including. Overview of the theory of real forms and strong real forms. This representation theory was initiated by brauer and it is more algebraic. Indecomposable representations of generalized weyl.
Introduction to representation theory of nite groups. Ivan penkov and vera serganova, generic irreducible representations of finitedimensional lie superalgebras, internat. If you have additional information or corrections regarding this mathematician, please use the update form. Gs10 caroline gruson and vera serganova, cohomology of generalized supergrassmannians and. A sentimental journey through representation theory. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. A contragredient lie superalgebra has finite growth if the dimensions of these graded components depend polynomially on the degree. Vera serganova department of mathematics, university of california at berkeley, berkeley, ca 94720, usa received 9 november 2001 communicated by susan montgomery abstract we introduce a new way to study representations of the lie superalgebra pn. Representation theory and symplectic singularities 4th8th april 2016, edinburgh timetable monday 4th 9.
Algebraic geometry and representation theory seminarroom 155. Representation theory and symplectic singularities 4th8th april 2016, edinburgh titles and abstracts monday 4th april 1011am stephen donkin, university of york title. The representation theory of the hecke algebra in type a can be. On the equivalence of two stability conditions of fbmodules. The connection between del pezzo surfaces and root systems goes back to coxeter and du val, and was given modern treatment by manin in his seminal book cubic forms. Representation theory and quantization titles and abstracts leticia barchini, oklahoma state university computing associated cycles of harishchandra modules, techniques and examples abstract. Algebraic geometry and representation theory seminar the. On the occasion of the 60th birthday of vitaly tarasov and the 70th birthday of alexander varchenko august 1216, 2019 eth, zurich, switzerland confirmed invited speakers. Del pezzo surfaces and representation theory vera serganova and alexei skorobogatov to yuri ivanovich manin on his 70th birthday abstract the connection between del pezzo surfaces and root systems goes back to coxeter and du val, and was given modern treatment by manin in his seminal book cubic forms.
To explain the many numerical coincidences batyrev conjectured. Representation theory of mackie lie algebras and their. Vera serganova representation theory for qn introduction the category qnmod equivalence of blocks blocks of category of nitedimensional q3modules main results ideas of proof bgg reciprocity outline 1 representation theory for qn introduction the category qnmod equivalence of blocks 2 blocks of category of nitedimensional q3modules main results. Algebraic geometry and representation theory seminar.
Batyrev conjectured that a universal torsor on a del pezzo surface can be embedded into a certain projective homogeneous space of the semisimple group with the same root system, equivariantly with respect to the maximal torus action. To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 32839 for the advisor id. Are there some fun applications of the theory of representations of finite groups. Mina aganagic uc berkeley, usa tomoyuki arakawa rims, japan. January 6 8, 2014 the weizmann institute of science, rehovot ziskind building, room 261 speakers. The talk is based on joint work with elizabeth dancohan and vera serganova. Representation theory and quantization university of toronto. In these notes we give an introduction to representation theory of simple finite. Vera serganova is a professor of mathematics at uc berkeley. The representation theory of the exceptional lie superalgebras f4 and g3 by lilit martirosyan doctor of philosophy in mathematics university of california, berkeley professor vera serganova, chair professor joseph wolf, cochair this thesis is a resolution.
Brundan found remarkable connections between the category f of. The text includes in particular infinitedimensional unitary representations for abelian groups, heisenberg groups and sl 2. Basic representation theory of finite groups and associative algebras. Del pezzo surfaces and representation theory request pdf. Then we focus on some classes of representations for which such. This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The theory has applications in many areas of mathematics, and lie algebras have been significant in the study of fundamental particles, including string theory, so this book should appeal to. Avraham aizenbud, rehovot joseph bernstein, tel aviv. The theme of this two week conference will be a survey of the state of the art in the use of cohomology and support in the study of representation theory, commutative algebra, triangulated categories, and various related topics. To submit students of this mathematician, please use the new data form. According to our current online database, vera serganova has 7 students and 7 descendants. A categorification of the bosonfermion correspondence via representation theory of sl1 igor frenkel, ivan penkov, and vera serganova abstract. We discuss the classification of finitegrowth contragredient lie superalgebras.
Vera serganova representation theory for qn introduction the category qnmod equivalence of blocks blocks of category of nitedimensional q3modules main results ideas of proof bgg reciprocity extension quiver for lie superalgebra q3 nikolay grantcharov1 advisor. Her research interests are in representation theory and algebraic geometry. Landmarks in representation theory caroline gruson and vera serganova. In the first talk, we describe the seminal example of springer representations, including. Skorobogatov to yuri ivanovich manin on his seventieth birthday the connection between del pezzo surfaces and root systems goes back to coxeter and du val, and was given modern treatment by manin in his seminal book cubic forms. The zeta function of monomial deformations of fermat hypersurfaces remke kloosterman. Algebraic geometry and representation theory seminar room 155. Minisymposium representation theory of lie superalgebras. These matrices enable us to extend the representationtheoretic approach of serganova and skorobogatov 14 from del pezzo surfaces to higher dimensions. Representation theory authorstitles recent submissions. The central object in geometric representation theory is a representation constructed from a variety, generally through a construction like cohomology that turns geometry into a vector space. Guide to the atlas software from the 2007 snowbird conference jeffrey adams this is a good practical introduction to the software. Vera teaches high and middle school students at berkeley math circle from 1998. In tame cases indecomposable modules are described.
In noncommutative geometry and representation theory in mathematical physics contemp. Ams representation theory of the american mathematical. Women in noncommutative algebra and representation. In the early 90s a class of algebras, known as double affine hecke algebras, were introduced by cherednik in connection with affine. The theory also becomes more uniform by focusing on surfaces over. Tensor representations of mackey lie algebras and their.
Lecture 4 schurweyl duality for dierent classical superalgebras. Speakers, speakersabstracts pdf, registration, accommodations. In mathematics, a cubic surface is a surface in 3dimensional space defined by one polynomial equation of degree 3. We discuss two types of invariants attached to a harishchandra module x, the associated variety and the. I would like to have some examples that could be explained to a student who knows what is a finite group but does not know much about what is a repersentation say knows the definition. A koszul category of representations of finitary lie algebras. In noncommutative geometry and representation theory. From finite groups to quivers via algebras caroline gruson, vera serganova this text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field.
Lie superalgebras and enveloping algebras, by ian musson. Del pezzo surfaces and representation theory vera serganova and alexei skorobogatov. Descent techniques in modular representation theory david benson, university of aberdeen, scotland modules of constant jordan type and vector bundles on projective spaces srikanth iyengar, university of nebraskalincoln commutative algebra for modular representations of finite groups. A journey through representation theory springerlink. Vera serganova university of california at berkeley borelweilbott theorem and bernsteingelfandgelfand reciprocity for classical supergroups abstract.
Part of this talk is based on joint work with karlhermann neeb. Vera serganova, kazhdanlusztig polynomials and character formula for the. Legendre polynomials naturally appear in the context of representation theory. The hecke algebras of finite and affine weyl groups arise naturally as convolution algebras associated to finite and locally compact groups, and play a prominent role in the representation theory of finite groups of lie type and of reductive padic groups. Category of germsp2nmodules with bounded weight multiplicities. The theory is simplified by working in projective space rather than affine space, and so cubic surfaces are generally considered in projective 3space. Abstract in these notes we give an introduction to representation theory of simple finitedimensional lie superalgebras. The mathematical sciences research institute msri, founded in 1982, is an independent nonprofit mathematical research institution whose funding sources include the national science foundation, foundations, corporations, and more than 90 universities and institutions.
For a class of generalized weyl algebras which includes the weyl algebras an a criterion is given as to when the category of indecomposable weight and generalized weight modules with supports from a fixed orbit is tame. Peterweyl theorem, principal bundles over lie groups, connections, chernsimons theory. In the theory of nite groups one can drop the assumption that the characteristic of the ground eld is zero. Cohomology and support in representation theory and related topics. Vera serganova berkeley on representations of the lie superalgebra pn.
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