Lax Operator for the Quantised Orthosymplectic Superalgebra U q [osp(m|n)]

Lax Operator for the Quantised Orthosymplectic

THE Q-q-SCHUR SUPERALGEBRA

As a natural generalisation of q-Schur algebras associated with the Hecke algebra Hr,R (of the symmetric group), we introduce the Q-q-Schur superalgebra associated with the Hecke-Clifford superalgebra H r,R, which, by definition, is the endomorphism algebra of the induced H r,R-module from certain q-permutation modules over Hr,R. We will describe certain integral bases for these superalgebras i...

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A Lax Operator Hierarchy for the New Fifth Order Integrable System

We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.

Lax operator for Macdonald symmetric functions

This is a joint work with Evgeny Sklyanin. Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q,t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the same variables and of the parameter t corresponding to th...