Rectangular Hall-Littlewood symmetric functions and a specific spin character

We derive the Schur function identities coming from the tensor products of the spin representations of the symmetric group Sn. We deal with the tensor products of the basic spin representation V (n) and any spin representation V λ (λ ∈ SP (n)). The characteristic map of the tensor product ζn ⊗ ζλ is described by Stembridge[4] for the case of odd n. We consider the case n is even

Brauer-Schur functions

A new class of functions is studied. We define the Brauer-Schur functions $B^{(p)}_{\lambda}$ for a prime number $p$, and investigate their properties. We construct a basis for the space of symmetric functions, which consists of products of $p$-Brauer-Schur functions and Schur functions. We will see that the transition matrix from the natural Schur function basis has some interesting numerical properties

Quantum Sylvester-Franke Theorem

A quantum version of classical Sylvester-Franke theorem is presented. After reviewing some representation theory of the quantum group GLq (n, C), the commutation relations of the matrix elements are verified. Once quantum determinant of the representation matrix is defined, the theorem follows naturall

Virasoro Action on Schur Q-function (Women in Mathematics)

Schur Q-function was introduced by Schur as a symmetric polynomial describing the irreducible index of the projective representation of a symmetric group. A formula for Schur Qfunctions is presented which describes the action of the Virasoro operators. For strict partition, we prove a formula for each LkQλ. and L_kQλ. (k ≥ 1), where Lk is the Virasoro operator. The present paper is a résumé of [1] and [2]

Compound basis arising from the basic A1(1)A^{(1)}_{1}-module

A new basis for the polynomial ring of infinitely many variables is constructed which consists of products of Schur functions and Q-functions. The transition matrix from the natural Schur function basis is investigated.Comment: 12 page

Brauer-Schur functions

A new class of functions is studied. We define the Brauer-Schur functions $B^{(p)}_{\lambda}$ for a prime number $p$, and investigate their properties. We construct a basis for the space of symmetric functions, which consists of products of $p$-Brauer-Schur functions and Schur functions. We will see that the transition matrix from the natural Schur function basis has some interesting numerical properties