A (-q)-analogue of weight multiplicities
We prove a conjecture in [L11] stating that certain polynomials P-Y(sigma),(w)(q) introduced in [LV11] for twisted involutions in an affine Weyl group give ( -q)-analogues of weight multiplicities of the Langlands dual group G. We also prove that the signature of a naturally defined hermitian form o...
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| Format: | Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/1721.1/124838 |
| _version_ | 1826207353873104896 |
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| author | Lusztig, George Yun, Zhiwei |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lusztig, George Yun, Zhiwei |
| author_sort | Lusztig, George |
| collection | MIT |
| description | We prove a conjecture in [L11] stating that certain polynomials P-Y(sigma),(w)(q) introduced in [LV11] for twisted involutions in an affine Weyl group give ( -q)-analogues of weight multiplicities of the Langlands dual group G. We also prove that the signature of a naturally defined hermitian form on each irreducible representation of e can be expressed in terms of these polynomials P-Y(sigma),(w)(q). |
| first_indexed | 2024-09-23T13:48:01Z |
| format | Article |
| id | mit-1721.1/124838 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:48:01Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | mit-1721.1/1248382020-04-24T03:13:45Z A (-q)-analogue of weight multiplicities Lusztig, George Yun, Zhiwei Massachusetts Institute of Technology. Department of Mathematics We prove a conjecture in [L11] stating that certain polynomials P-Y(sigma),(w)(q) introduced in [LV11] for twisted involutions in an affine Weyl group give ( -q)-analogues of weight multiplicities of the Langlands dual group G. We also prove that the signature of a naturally defined hermitian form on each irreducible representation of e can be expressed in terms of these polynomials P-Y(sigma),(w)(q). National Science Foundation (U.S.) (Grant DMS-0758262) National Science Foundation (U.S.) (Grant DMS-0969470) 2020-04-23T17:31:38Z 2020-04-23T17:31:38Z 2012-03 2020-03-31T17:07:08Z Article http://purl.org/eprint/type/JournalArticle 2320-3110 0970-1249 https://hdl.handle.net/1721.1/124838 Lusztig, George and Zhiwei Yun. “A (-q)-analogue of weight multiplicities.” Journal of the Ramanujan Mathematical Society 28A (2012) en Journal of the Ramanujan Mathematical Society Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf arXiv |
| spellingShingle | Lusztig, George Yun, Zhiwei A (-q)-analogue of weight multiplicities |
| title | A (-q)-analogue of weight multiplicities |
| title_full | A (-q)-analogue of weight multiplicities |
| title_fullStr | A (-q)-analogue of weight multiplicities |
| title_full_unstemmed | A (-q)-analogue of weight multiplicities |
| title_short | A (-q)-analogue of weight multiplicities |
| title_sort | q analogue of weight multiplicities |
| url | https://hdl.handle.net/1721.1/124838 |
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