A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type BCn
نویسندگان
چکیده
Let G = GL(N), K = GL(p)× GL(q), where p + q = N , and let n be a positive integer. We construct a functor from the category of HarishChandra modules for the pair (G,K) to the category of representations of the degenerate affine Hecke algebra of type Bn, and a functor from the category of K-monodromic twisted D-modules on G/K to the category of representations of the degenerate double affine Hecke algebra of type BCn; the second functor is an extension of the first one.
منابع مشابه
ON SOME REPRESENTATIONS OF DEGENERATE AFFINE HECKE ALGEBRAS OF TYPE BCn
The degenerate affine Hecke algebra (dAHA) of any finite Coxeter group was defined by Drinfeld and Lusztig([Dri],[Lus]). It is generated by the group algebra of the Coxeter group and by the commuting generators yi with some relations. In [AS], the authors give a Lie-theoretic construction of representations of the dAHA of type An−1. They construct a functor from the BGG category of slN to the c...
متن کاملRealization of locally extended affine Lie algebras of type $A_1$
Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...
متن کاملA LIE-THEORETIC CONSTRUCTION OF REPRESENTATIONS OF THE DEGENERATE AFFINE AND DOUBLE AFFINE HECKE ALGEBRAS OF TYPE BCn
The degenerate affine Hecke algebra (dAHA) of any Coxeter group was defined by Drinfeld and Lusztig([Dri],[Lus]). It is generated by the group algebra of the Coxeter group and by the commuting generators yi with some relations. The degenerate double affine Hecke algebra (dDAHA) of a root system was introduced by Cherednik (see [Ch]). It is generated by the the group algebra of the Weyl group, c...
متن کامل2 1 A pr 1 99 8 LIE ALGEBRAS AND DEGENERATE AFFINE HECKE ALGEBRAS OF TYPE
We construct a family of exact functors from the BernsteinGelfand-Gelfand category O of sln-modules to the category of finite-dimensional representations of the degenerate affine Hecke algebra Hl of GLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple Hl-module can be thus obtained. Introduction The classical Frobenius...
متن کاملDegenerate Double Affine Hecke Algebra And Conformal Field Theory
We introduce a class of induced representations of the degenerate double affine Hecke algebra H of glN (C) and analyze their structure mainly by means of intertwiners of H . We also construct them from ŝlm(C)-modules using Knizhnik-Zamolodchikov connections in the conformal field theory. This construction provides a natural quotient of induced modules, which turns out to be the unique irreducib...
متن کامل