Fused Specht Polynomials and $c=1$ Degenerate Conformal Blocks
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 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 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.
Cite
@article{arxiv.2410.09798,
title = {Fused Specht Polynomials and $c=1$ Degenerate Conformal Blocks},
author = {Augustin Lafay and Eveliina Peltola and Julien Roussillon},
journal= {arXiv preprint arXiv:2410.09798},
year = {2025}
}
Comments
v3 (final): clarified the proof of Lemma 3.2, and made minor edits. To appear in Trans. AMS