Tensor powers of vector representation of $U_q(\mathfrak{sl}_2)$ at even roots of unity
| Autor: | Lachowska, Anna, Postnova, Olga, Reshetikhin, Nicolai, Solovyev, Dmitry |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the decomposition of tensor powers of two dimensional irreducible representations of quantum $\mathfrak{sl}_2$ at even roots of unity into direct sums of tilting modules. We derive a combinatorial formula for multiplicity of tilting modules in the $N$-th tensor power of two dimensional irreducible representations, interpret it in terms of lattice paths and find its asymptotic behavior when $N\to\infty$. We also describe the limit of character and Plancherel measures when $N\to\infty$. We consider both $U_q(\mathfrak{sl}_2)$ with divided powers and the small quantum $sl_2$. Comment: 43 pages |
| Databáze: | arXiv |
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