Yangians, Mirabolic Subalgebras, and Whittaker Vectors
We construct an element in a completion of the universal enveloping algebra of N, which we call the Kirillov projector, that connects the topics of the title: on the one hand, it is defined using the evaluation homomorphism from the Yangian of N, on the other hand, it gives a canonical projection on...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2025 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2025
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/213188 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Yangians, Mirabolic Subalgebras, and Whittaker Vectors. Artem Kalmykov. SIGMA 21 (2025), 025, 54 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We construct an element in a completion of the universal enveloping algebra of N, which we call the Kirillov projector, that connects the topics of the title: on the one hand, it is defined using the evaluation homomorphism from the Yangian of N, on the other hand, it gives a canonical projection onto the space of Whittaker vectors for any Whittaker module over the mirabolic subalgebra. Using the Kirillov projector, we deduce some categorical properties of Whittaker modules; for instance, we prove a mirabolic analog of Kostant's theorem. We also show that it quantizes a rational version of the Cremmer-Gervais -matrix. As an application, we construct a universal vertex-IRF transformation from the standard dynamical -matrix to this constant one in categorical terms.
|
|---|---|
| ISSN: | 1815-0659 |