Crystal Bases for the Quantum Superalgebra $U_q(D(N,1))$, $U_q(B(N,1))$
| dc.creator | Suzuki, Kenei | |
| dc.date | 2003-03-11 | |
| dc.date.accessioned | 2026-07-07T04:55:55Z | |
| dc.date.available | 2026-07-07T04:55:55Z | |
| dc.description | Let $V(λ)$ be the irreducible lowest weight $U_q(D(N,1))$-module with lowest weight $λ$. Assume $λ= n_0ω_0-\sum_{i=0}^{N}n_iω_i$, where $ω_0$ is the fundamental weight corresponding to the unique odd coroot $h_0$, and $n_i$ are positive integers. $V(λ)$ is called typical if $n_0 \geq 0$. In this paper, we construct polarizable crystal bases of $V(λ)$ in the category ${\cal O}_{int}$, which is a class of integrable modules. We also describe the decomposition of the tensor product of typical representations into irreducible ones, using the generalized Littlewood-Richardson rule for $U_q(D(N))$. We also present analogous results for the quantum superalgebra $U_q(B(N,1))$. | |
| dc.description | 28 pages, 5 figures, platex | |
| dc.identifier | https://arxiv.org/abs/math/0303124 | |
| dc.identifier | http://arxiv.org/abs/math/0303124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66751 | |
| dc.subject | Quantum Algebra | |
| dc.title | Crystal Bases for the Quantum Superalgebra $U_q(D(N,1))$, $U_q(B(N,1))$ | |
| dc.type | text |