The freeness and trace conjectures for parabolic Hecke subalgebras

Bethe Subalgebras in Hecke Algebra and Gaudin Models Bethe Subalgebras in Hecke Algebra and Gaudin Models

The generating function for elements of the Bethe subalgebra of Hecke algebra is constructed as Sklyanin's transfer-matrix operator for Hecke chain. We show that in a special classical limit q → 1 the Hamiltonians of the Gaudin model can be derived from the transfer-matrix operator of Hecke chain. We consruct a non-local analogue of the Gaudin Hamiltonians for the case of Hecke algebras.

Primitivity, freeness, norm and trace

Hecke Algebra Characters and Immanant Conjectures

The main purpose of this article is to announce and provide supporting evidence for two conjectures about the characters of the Hecke algebra Hn(q) of type An_I' evaluated at elements of its Kazhdan-Lusztig basis. In addition, we prove a conjectured immanant inequality for Jacobi-Trudi matrices (definitions below) and show how our conjectures would imply stronger inequalities of a similar kind....

Nilpotent Orbits and Theta-stable Parabolic Subalgebras

In this work, we present a new classification of nilpotent orbits in a real reductive Lie algebra g under the action of its adjoint group. Our classification generalizes the Bala-Carter classification of the nilpotent orbits of complex semisimple Lie algebras. Our theory takes full advantage of the work of Kostant and Rallis on pC , the “complex symmetric space associated with g”. The Kostant-S...

2 The Trace Formula and Hecke Operators

This lecture is intended as a general introduction to the trace formula. We shall describe a formula that is a natural generalization of the Selberg trace formula for compact quotient. Selberg also established trace formulas for noncompact quotients of rank 1, and our formula can be regarded as an analogue for general rank of these. As an application, we shall look at the "finite case" of the t...