Baxter Operator and Archimedean Hecke Algebra

Baxter operator and Archimedean Hecke algebra

In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gll+1 and so2l+1. Whittaker functions corresponding to these algebras are eigenfunctions of the Q-operators with the eigenvalues expressed in terms of Gammafunctions. The appearance of the Gamma-functions is one of the manifestations of an interesting connection between Mellin-Barnes and Givental integral...

From Baxter operator to Archimedean Hecke algebra

In this note we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gll+1 and so2l+1. Corresponding Whittaker functions are eigenfunctions of the Q-operators with the eigenvalues expressed in terms of Gamma-functions. This property is one of the manifestations of an interesting connection between MellinBarnes and Givental integral representations of Whittaker functions. Th...

The affine Hecke algebra

1 The affine Hecke algebra 1.1 The alcove walk algebra Fix notations for the Weyl group W , the extended affine Weyl group W , and their action on Ω × h * R as in Section 2. Label the walls of the alcoves so that the fundamental alcove has walls labeled 0, 1,. .. , n and the labeling is W-equivariant (see the picture in (2.12)). The periodic orientation is the orientation of the walls of the al...

Hecke Algebra Characters

Hecke Algebra Actions on the Coinvariant Algebra

Two actions of the Hecke algebra of type A on the corresponding polynomial ring are introduced. Both are deformations of the natural action of the symmetric group on polynomials, and keep symmetric functions invariant. An explicit combinatorial formula is given for the resulting graded characters on the coinvariant algebra.