Graded characters, demazure multiplicities, and chebyshev polynomials
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917461968814080 |
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| author | Biswal, Rekha |
| author_facet | Biswal, Rekha |
| contents | In this paper, we study numerical multiplicities of Demazure modules in the excellent filtration of $\mathfrak{sl}_2[t]$-modules $V(ξ)$, where $V(ξ)$ denotes the fusion product associated to a partition $ξ$. We express generating functions for the numerical multiplicities of level $m$ Demazure modules in excellent filtrations of $V(ξ)$ in terms of quotients of Chebyshev polynomials, thereby generalizing earlier results for fat hook partitions.
We also revisit the graded multiplicities of irreducible $\mathfrak{sl}_2$-modules in $V(ξ)$ and provide a new and self-contained proof of their description in terms of cocharge Kostka--Foulkes polynomials. While this connection has been established in earlier works, our approach is elementary and relies only on recursive structures arising from short exact sequences of fusion products. As a consequence, we obtain a direct and self-contained derivation of the graded characters of $V(ξ)$ in terms of Hall--Littlewood polynomials with coefficients given by cocharge Kostka--Foulkes polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graded characters, demazure multiplicities, and chebyshev polynomials Biswal, Rekha Representation Theory In this paper, we study numerical multiplicities of Demazure modules in the excellent filtration of $\mathfrak{sl}_2[t]$-modules $V(ξ)$, where $V(ξ)$ denotes the fusion product associated to a partition $ξ$. We express generating functions for the numerical multiplicities of level $m$ Demazure modules in excellent filtrations of $V(ξ)$ in terms of quotients of Chebyshev polynomials, thereby generalizing earlier results for fat hook partitions. We also revisit the graded multiplicities of irreducible $\mathfrak{sl}_2$-modules in $V(ξ)$ and provide a new and self-contained proof of their description in terms of cocharge Kostka--Foulkes polynomials. While this connection has been established in earlier works, our approach is elementary and relies only on recursive structures arising from short exact sequences of fusion products. As a consequence, we obtain a direct and self-contained derivation of the graded characters of $V(ξ)$ in terms of Hall--Littlewood polynomials with coefficients given by cocharge Kostka--Foulkes polynomials. |
| title | Graded characters, demazure multiplicities, and chebyshev polynomials |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2604.17437 |