Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials
Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials
Abstract We construct a family of representations of affine Hecke algebras, which depend on a number of auxiliary parameters $$g_i$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>g</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math> , and which we refer to as metaplectic representations. We realize these representations as quotients of certain parabolically induced modules, and we apply the method of Baxterization (localization) …