We consider two types of quotients of the integrable modules of sl 2. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level k. We describe monomial bases for the spaces of coinvariants, which leads to a fermionic description of these spaces. For k = 1, we give explicit formulas for the characters. We also present recursion relations satisfied by the ch...

In this paper we construct bases of standard modules L(Λ) for affine Lie algebra of type B (1) 2 consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for FeiginStoyanovsky’s subspaces W (Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W (kΛ0) for B (1) 2 and the standard module L...

G. E. Murphy showed in 1983 that the centre of every symmetric group algebra has an integral basis consisting of a specific set of monomial symmetric polynomials in the Jucys–Murphy elements. While we have shown in earlier work that the centre of the group algebra of S3 has exactly three additional such bases, we show in this paper that the centre of the group algebra of S4 has infinitely many ...

Given n polynomials in n variables of respective degrees d1, . . . , dn, and a set of monomials of cardinality d1 . . . dn, we give an explicit subresultant-based polynomial expression in the coefficients of the input polynomials whose non-vanishing is a necessary and sufficient condition for this set of monomials to be a basis of the ring of polynomials in n variables modulo the ideal generate...

Using Nakajima’s monomials, we construct a new realization of crystal bases for finite dimensional irreducible modules over quantum classical algebras. We also give an explicit bijection between the monomial realization and the Young tableau realization of crystal bases.