Congruence for lattice path models with filter restrictions and long steps
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909162437345280 |
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| author | Solovyev, Dmitry |
| author_facet | Solovyev, Dmitry |
| contents | We derive a path counting formula for two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves a problem of finding an explicit formula for multiplicities of modules in tensor product decomposition of $T(1)^{\otimes N}$ for $U_q(sl_2)$ with divided powers, where $q$ is a root of unity. Combinatorial treatment of this problem calls for definition of congruence of regions in lattice path models, properties of which are explored in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_13857 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Congruence for lattice path models with filter restrictions and long steps Solovyev, Dmitry Combinatorics Representation Theory 05E10, 16T30, 05A15, 05A19 We derive a path counting formula for two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves a problem of finding an explicit formula for multiplicities of modules in tensor product decomposition of $T(1)^{\otimes N}$ for $U_q(sl_2)$ with divided powers, where $q$ is a root of unity. Combinatorial treatment of this problem calls for definition of congruence of regions in lattice path models, properties of which are explored in this paper. |
| title | Congruence for lattice path models with filter restrictions and long steps |
| topic | Combinatorics Representation Theory 05E10, 16T30, 05A15, 05A19 |
| url | https://arxiv.org/abs/2111.13857 |