HIGHEST-WEIGHT VECTORS FOR THE ADJOINT ACTION OF GL n ON POLYNOMIALS, II

HIGHEST-WEIGHT VECTORS FOR THE ADJOINT ACTION OF GLn ON POLYNOMIALS, II

HIGHEST WEIGHT VECTORS OF IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERALGEBRA Uq (gl(m,n))

The Iwahori-Hecke algebra Hk(q ) of type A acts on tensor product space V ⊗k of the natural representation of the quantum superalgebra Uq(gl(m, n)). We show this action of Hk(q ) and the action of Uq(gl(m, n)) on the same space determine commuting actions of each other. Together with this result and Gyoja’s q-analogue of the Young symmetrizer, we construct a highest weight vector of each irredu...

Generalized Drinfeld Polynomials for Highest Weight Vectors of the Borel Subalgebra of the Sl2 Loop Algebra

In a Borel subalgebra U(B) of the sl2 loop algebra, we introduce a highest weight vector Ψ. We call such a representation of U(B) that is generated by Ψ highest weight. We define a generalization of the Drinfeld polynomial for a finitedimensional highest weight representation of U(B). We show that every finitedimensional highest weight representation of the Borel subalgebra is irreducible if th...

math.QA/9908008 Vertex Operators of Uq[ ̂ gl(N|N)] and Highest Weight Representations of Uq[

We determine the exchange relations of the level-one q-vertex operators of the quantum affine superalgebra Uq[ ̂ gl(N |N)]. We study in details the level-one irreducible highest weight representations of Uq[ ̂ gl(2|2)], and compute the characters and supercharacters associated with these irreducible modules. Mathematics Subject Classifications (1991): 17B37, 81R50, 81R10, 16W30

REPRESENTATIONS OF THE QUANTUM TOROIDAL ALGEBRA ON HIGHEST WEIGHT MODULES OF THE QUANTUM AFFINE ALGEBRA OF TYPE gl N

A representation of the quantum toroidal algebra of type sl N is de ned on every integrable irreducible highest weight module of the the quantum a ne algebra of type gl N : The q-version of the level-rank duality giving the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U 0 q ( b gl N ) of level L and U 0 q ( b sl L ) of level N is described.