豪二象性与动态Weyl群。

IF 0.6 3区数学 Q4 MATHEMATICS

Transformation Groups Pub Date : 2026-01-01 Epub Date: 2024-12-06 DOI:10.1007/s00031-024-09888-7

Rea Dalipi, Giovanni Felder, Anfisa Gurenkova

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引用次数: 0

摘要

我们给出了U q （gl ^ N）的向量表示的外幂的r矩阵的费米子公式，并通过Howe （gl N, gl M）对偶性将其与Tarasov-Varchenko和Etingof-Varchenko的动态Weyl群联系起来。在极限N→∞下，我们得到了Fock空间的r矩阵。根据我们的结果，我们得到了Weyl群在可积U q gl M -模上的一个动态作用，推广了已知的零权空间上的作用。在Anfisa Gurenkova的附录中，证明了如果用一般的可对称的Kac-Moody代数代替gl M，后一个性质也成立。

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Howe Duality and Dynamical Weyl Group.

We give a fermionic formula for R-matrices of exterior powers of the vector representations of $U_{q} ({\hat{gl}}_{N})$ and relate it to the dynamical Weyl group of Tarasov-Varchenko and Etingof-Varchenko, via a Howe ( ${gl}_{N}, {gl}_{M})$ -duality. In the limit $N \to \infty$ we obtain R-matrices for Fock spaces. As a consequence of our result we obtain a dynamical action of the Weyl group on integrable $U_{q} {gl}_{M}$ -modules, extending the known action on zero weight spaces. In an Appendix by Anfisa Gurenkova it is shown that the latter property also holds if we replace ${gl}_{M}$ by a general symmetrizable Kac-Moody algebra.

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来源期刊

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.