An inversion formula for some Fock spaces

Abstract

A symmetric bilinear form on a certain subspace ${\hat{\mathbb{T}}}^{\mathbf{b}}$ of a completion of the Fock space ${\mathbb{T}}^{\mathbf{b}}$ is defined. The canonical and dual canonical bases of ${\hat{\mathbb{T}}}^{\mathbf{b}}$ are dual with respect to the bilinear form. As a consequence, the inversion formula connecting the coefficients of the canonical basis and that of the dual canonical basis of ${\hat{\mathbb{T}}}^{\mathbf{b}}$ expanded in terms of the standard monomial basis of ${\mathbb{T}}^{\mathbf{b}}$ is obtained. Combining with the Brundan's algorithm for computing the elements in the canonical basis of ${\hat{\mathbb{T}}}^{{\mathbf{b}}_{\mathrm{st}}}$, we have an algorithm computing the elements in the canonical basis of ${\hat{\mathbb{T}}}^{\mathbf{b}}$ for arbitrary $\mathbf{b}$.

23 pages

References in corpus (1)

• Tensor product categorifications and the super Kazhdan-Lusztig conjecture

Cited by in corpus (3)

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