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September 10, 2025Open Access

Fused Specht polynomials and 𝑐=1 degenerate conformal blocks

ALAugustin LafayAalto University EPEveliina PeltolaUniversity of Geneva JRJulien RoussillonAalto University

Key Points

Fused Specht polynomials characterize irreducible representations of the fused Hecke algebra.
The polynomials construct a basis for holomorphic conformal blocks with central charge c=1.
Conformal field theory implications arise from the associated correlation functions.
This research connects degenerate primary fields to invariant boundary conditions for the Gaussian free field.

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 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 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.

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