Representation Theory Seminar
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Thu, 19/01/2012 14:00 |
Shamgar Gurevich (Madison) |
Representation Theory Seminar  |
L3 |
| This is a sequel to Lecture I (given in the algebra seminar, Tuesday). It will be slightly more specialized. The finite Weil representation is the algebra object that governs the symmetries of the Hilbert space H =C(Z/p): The main objective of this talk is to introduce the geometric Weil representation which is an algebra-geometric (l-adic perverse Weil sheaf) counterpart of the finite Weil representation. Then, I will explain how the geometric Weil representation is used to prove the main technical results stated in Lecture I. In the course, I will explain the Grothendieck geometrization procedure by which sets are replaced by algebraic varieties and functions by sheaf theoretic objects. This is a joint work with R. Hadani (Austin). | |||
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Thu, 26/01/2012 14:00 |
Alexey Sevastyanov (Aberdeen) |
Representation Theory Seminar |
L3 |
| De Concini-Kac-Procesi conjecture gives a good estimate for the dimensions of finite–dimensional non-restricted representations of quantum groups at m-th root of unity. According to De Concini, Kac and Procesi such representations can be split into families parametrized by conjugacy classes in an algebraic group G, and the dimensions of representations corresponding to a conjugacy class O are divisible by m^{dim O/2}. The talk will consist of two parts. In the first part I shall present an approach to the proof of De Concini-Kac-Procesi conjecture based on the use of q-W algebras and Bruhat decomposition in G. It turns out that properties of representations corresponding to a conjugacy class O depend on the properties of intersection of O with certain Bruhat cells. In the second part, which is more technical, I shall discuss q-W algebras and some related results in detail. | |||
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Fri, 17/02/2012 12:00 |
David Craven, Oxford. (Bloc meeting). |
Representation Theory Seminar |
L2 |
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Fri, 17/02/2012 15:00 |
Anton Cox, City University (Bloc meeting) |
Representation Theory Seminar |
L1 |
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Fri, 17/02/2012 16:30 |
Shigeo Koshitani, Chiba University, Japan. (Bloc meeting) |
Representation Theory Seminar |
L3 |
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Thu, 23/02/2012 14:00 |
Emmanuele Letellier (Caen) |
Representation Theory Seminar |
L3 |
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Thu, 08/03/2012 15:00 |
John Duncan |
Representation Theory Seminar |
L3 |
| In April 2010 Eguchi–Ooguri–Tachikawa observed a fascinating connection between the elliptic genus of a K3 surface and the largest Mathieu group. We will report on joint work with Miranda Cheng and Jeff Harvey that identifies this connection as one component of a system of surprising relationships between a family of finite groups, their representation theory, and automorphic forms of various kinds Mock modular forms, and particularly their shadows, play a key role in the analysis, and we find several of Ramanujan's mock theta functions appearing as McKay–Thompson series arising from the umbral groups. | |||
