Gaudin subalgebras and wonderful models

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.

Wonderful Models of Subspace Arrangements

0 Introduction In this paper we describe, for any given nite family of sub-spaces of a vector space or for linear subspaces in aane or projective space, a smooth model, proper over the given space, in which the complement of these subspaces is unchanged but the family of subspaces is replaced by a divisor with normal crossings. This model can be described explicitly in a combinatorial way and a...

Integrable Richardson-Gaudin models in mesoscopic physics

Integrable Richardson-Gaudin models in mesoscopic physics

Integrable Richardson-Gaudin models in mesoscopic physics