Howe duality and dynamical Weyl group
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916404117110784 |
|---|---|
| author | Dalipi, Rea Felder, Giovanni |
| author_facet | Dalipi, Rea Felder, Giovanni |
| contents | We give a fermionic formula for $R$-matrices of exterior powers of the vector representations of $U_q(\widehat{ \mathfrak{gl}}_N)$ and relate it to the dynamical Weyl group of Tarasov--Varchenko and Etingof--Varchenko, via a Howe ($\mathfrak{gl}_N,\mathfrak{gl}_M)$-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 $U_q\mathfrak{gl}_M$-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 $\mathfrak{gl}_M$ by a general symmetrizable Kac--Moody algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13055 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Howe duality and dynamical Weyl group Dalipi, Rea Felder, Giovanni Representation Theory 17B37 We give a fermionic formula for $R$-matrices of exterior powers of the vector representations of $U_q(\widehat{ \mathfrak{gl}}_N)$ and relate it to the dynamical Weyl group of Tarasov--Varchenko and Etingof--Varchenko, via a Howe ($\mathfrak{gl}_N,\mathfrak{gl}_M)$-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 $U_q\mathfrak{gl}_M$-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 $\mathfrak{gl}_M$ by a general symmetrizable Kac--Moody algebra. |
| title | Howe duality and dynamical Weyl group |
| topic | Representation Theory 17B37 |
| url | https://arxiv.org/abs/2208.13055 |