Lecture 1: Reminder on Affine Hecke Algebras
نویسنده
چکیده
These are notes for a seminar talk at the MIT-Northeastern Spring 2017 Double Affine Hecke Algebras and Elliptic Hall Algebras (DAHAEHA) Seminar.
منابع مشابه
Spin Hecke Algebras of Finite and Affine Types
We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine) Hecke-Clifford algebras of Olshanski and Jones-Nazarov. Relation between the spin (affine) Hecke algebra and a nonstandard presentation of the usual (affine) Hecke alge...
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These are notes for a talk in the MIT-NEU Graduate seminar on Hecke Algebras and Affine Hecke Algebras (AHAHA) held in Fall 2014. This talk is divided into three parts. In the first, we introduce the affine Hecke algebras and describe a useful basis for the algebra over the ground ring. We then give a complete description of the center of the affine Hecke algebra and prove Kato’s Theorem regard...
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The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irre-ducible unitarizable representations are classified.
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The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role. This result is essential for the theory of intertwiners of double affine Hecke algebras.
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The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie algebra g where g is gl ∞ or the affine Lie algebra A (1) l , and the irreducible representations correspond to the upper global bases. Recently, N. Enomoto an...
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