Homological realization of the restricted Kostka polynomials

B. Feigin; E. Feigin

Home/Archive/arXiv

arXiv · math/0503058

Homological realization of the restricted Kostka polynomials

B. Feigin·E. Feigin

View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper we give two realizations of the restricted Kostka polynomials for $\sl_2$. Firstly we identify the restricted Kostka polynomials with a characters of the zero homology of the current algebra with a coefficients in a certain modules. As a corollary we reobtain the alternating sum formula. Secondly we show that the restricted Kostka polynomials are a $q$-multiplicities of the decomposition of the certain integrable $\hat{\sl}_2$-modules to the irreducible components. This allows to write a kind of fermionic formula for the Virasoro unitary models.

Explore related subjects

math.QA math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

B. Feigin, E. Feigin. 2006-01-09. Homological realization of the restricted Kostka polynomials. https://arxiv.org/abs/math/0503058

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Maximality Levels of the classical permutation group in the quantum permutation group

Progress on the conjecture of Banica and Bichon that the classical permutation group is a maximal quantum subgroup of the quantum permutation group remains limited to a handful of small-parameter results. By Tannaka--Krein duality, any counterexample to this Maximality Conjecture must arise from a category strictly intermediate between the category $\mathcal{NC}$ of non-crossing partitions and the category $\mathcal{P}$ of all partitions. Any such exotic category must therefore contain a linear combination of crossing-partition vectors. The categories generated by $\mathcal{NC}$ together with some such vectors are studied, with a number of generation results. It is shown that no exotic category can contain a linear combination of three crossing-partition vectors, and, using an argument of ChatGPT to account for a five-dimensional gap, there is no exotic category distinguished from $\mathcal{NC}$ or $\mathcal{P}$ at moments of order six.

math.QA↗

arXiv2026

Pre-modular fusion categories of global dimension $2p$

Let $p>5$ be a prime. In this paper, we show that a pre-modular fusion category of global dimension $2p$ is either pointed or tensor equivalent to $\text{Rep}(D_{2p})$.

math.QA↗

arXiv2026

Graded Automorphism of Multiparameter Quantum Matrix Algebra

We determine the graded automorphism group of the multiparameter quantum matrix algebra $\mathcal O_{λ,\mathbf p}(M_n(\Bbbk))$ over an arbitrary field $\Bbbk$ for all $n\ge2$ and $λ\ne1$. No other restrictions are assumed on $\mathbf p$ or $λ$. Every graded automorphism is a torus automorphism, possibly followed by transposition or by simultaneous reversal of the row and column indices. We give the precise parameter conditions for these two involutions. As an application, we also determine the full automorphism group when the multiplicative group generated by the parameters is torsion-free.

math.QA↗