Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Methods in Representation Theory of Hecke Algebras and Quantum
  Groups   These lectures given in Montreal in Summer 1997 are mainly based on, and form
a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation
Theory and Complex Geometry', Birkhauser 1997.
  Various algebras arising naturally in Representation Theory such as the group
algebra of a Weyl group, the universal enveloping algebra of a complex
semisimple Lie algebra, a Quantum group or the Iwahori-Hecke algebra of
bi-invariant functions (under convolution) on a p-adic group, are considered.
  We give a uniform geometric construction of these algebras in terms of
homology of an appropriate "Steinberg-type" variety Z (or its modification,
such as K-theory or elliptic cohomology of Z, or an equivariant version
thereof). We then explain how to obtain a complete classification of finite
dimensional irreducible representations of the algebras in question, using our
geometric construction and perverse sheaves methods.
  Similar techniques can be applied to other algebras, e.g. the Double-affine
Hecke algebras, Elliptic algebras, quantum toroidal algebras.

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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio