Abstract
Let (Formula presented.) be the Yangian associated to the general linear Lie algebra (Formula presented.), defined over an algebraically closed field (Formula presented.) of characteristic (Formula presented.). In this paper, we study the representation theory of the restricted Yangian (Formula presented.). This leads to a description of the representations of (Formula presented.), whose (Formula presented.) -character is nilpotent with Jordan type given by a two-row partition (Formula presented.).
| Original language | English |
|---|---|
| Article number | e70056 |
| Journal | Journal of the London Mathematical Society |
| Volume | 111 |
| Issue number | 1 |
| Early online date | 16 Dec 2024 |
| DOIs | |
| Publication status | Published - 31 Jan 2025 |
Funding
The authors would like to thank Simon Goodwin and Adam Thomas for useful conversations and correspondence, and for sharing details of their forthcoming work on this topic. The first author is supported partially by NSFC (grant nos. 12071168, 12461005), the Fundamental Research Funds for the Central Universities (nos. CCNU22QN002, CCNU24JC001), China Scholarship Council (no. 202306770031) and Key Laboratory of MEA, Ministry of Education. He would like to thank Department of Mathematical Sciences at University of Bath for their hospitality and support. The third author is supported by a UKRI Future Leaders Fellowship, grant numbers MR/S032657/1, MR/S032657/2, MR/S032657/3.
| Funders | Funder number |
|---|---|
| Fundamental Research Funds for the Central Universities | CCNU24JC001, CCNU22QN002 |
| UK Research and Innovation | MR/S032657/3, MR/S032657/1, MR/S032657/2 |
| National Natural Science Foundation of China | 12461005, 12071168 |
| China Scholarship Council | 202306770031 |