Fused Specht Polynomials and $c=1$ Degenerate Conformal Blocks

TL;DR

This paper introduces fused Specht polynomials to characterize representations of the fused Hecke algebra at q=-1 and constructs a basis for degenerate conformal blocks with central charge c=1, linking algebraic and conformal field theory structures.

Contribution

It develops fused Specht polynomials and applies them to construct bases for conformal blocks with specific degeneracy and central charge, connecting algebraic and conformal field theory insights.

Findings

Characterization of irreducible representations of fused Hecke algebra at q=-1

Construction of a basis for degenerate conformal blocks with c=1

Correlation functions potentially yield conformally invariant boundary conditions

Abstract

We introduce a class of polynomials that we call fused Specht polynomials and use them to characterize irreducible representations of the fused Hecke algebra with parameter $q=-1$ in the space of polynomials. We apply the fused Specht polynomials to construct a basis for a space of holomorphic (chiral) conformal blocks with central charge $c=1$ which are degenerate at each point. In conformal field theory, this corresponds to all primary fields having conformal weight in the Kac table. The associated correlation functions are expected to give rise to conformally invariant boundary conditions for the Gaussian free field, which has also been verified in special cases.