Generic character sheaves on groups over k[∊]/[∊]r
Let k be an algebraic closure of the finite field F[subscript q] with q elements where q is a power of a prime number p. Let G be a connected reductive group over k with a fixed split F[subscript q]-rational structure, a fixed Borel subgroup B defined over F[subscript q], with unipotent radical U an...
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| Format: | Article |
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AMS
2020
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| Online Access: | https://hdl.handle.net/1721.1/124911 |
| _version_ | 1826217305094225920 |
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| author | Lusztig, George |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lusztig, George |
| author_sort | Lusztig, George |
| collection | MIT |
| description | Let k be an algebraic closure of the finite field F[subscript q] with q elements where q is a power of a prime number p. Let G be a connected reductive group over k with a fixed split F[subscript q]-rational structure, a fixed Borel subgroup B defined over F[subscript q], with unipotent radical U and a fixed maximal torus T of B defined over F[subscript q]. Let g, b, t, n be the Lie algebras of G, B, T, U. We fix a prime number l ≠ p. If λ : T(F[subscript q]) → [line over Q][subscript * under superscript l] is a character, we can lift λ to a character λ˜ : B(F[subscript q]) → [line over Q][subscript * under superscript l] trivial on U(F[subscript q]) and we can form the induced representation [mathematical figure; see resource] of G(F[subscript q]). [First paragraph] ©2017 |
| first_indexed | 2024-09-23T17:01:19Z |
| format | Article |
| id | mit-1721.1/124911 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T17:01:19Z |
| publishDate | 2020 |
| publisher | AMS |
| record_format | dspace |
| spelling | mit-1721.1/1249112022-09-29T23:09:07Z Generic character sheaves on groups over k[∊]/[∊]r Lusztig, George Massachusetts Institute of Technology. Department of Mathematics Let k be an algebraic closure of the finite field F[subscript q] with q elements where q is a power of a prime number p. Let G be a connected reductive group over k with a fixed split F[subscript q]-rational structure, a fixed Borel subgroup B defined over F[subscript q], with unipotent radical U and a fixed maximal torus T of B defined over F[subscript q]. Let g, b, t, n be the Lie algebras of G, B, T, U. We fix a prime number l ≠ p. If λ : T(F[subscript q]) → [line over Q][subscript * under superscript l] is a character, we can lift λ to a character λ˜ : B(F[subscript q]) → [line over Q][subscript * under superscript l] trivial on U(F[subscript q]) and we can form the induced representation [mathematical figure; see resource] of G(F[subscript q]). [First paragraph] ©2017 2020-04-28T19:13:43Z 2020-04-28T19:13:43Z 2017 Article http://purl.org/eprint/type/JournalArticle 1098-3627 https://hdl.handle.net/1721.1/124911 Lusztig, G., "Generic character sheaves on groups over k[∊]/[∊]r." In Beliakova, Anna, and Aaron D. Lauda, eds., Categorification and Higher Representation Theory (Providence, R.I.: American Mathematical Society, 2017): p. 227-46 ©2017 Author(s) https://www.ams.org/books/conm/683/conm683-endmatter.pdf Categorification and Higher Representation Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf AMS arXiv |
| spellingShingle | Lusztig, George Generic character sheaves on groups over k[∊]/[∊]r |
| title | Generic character sheaves on groups over k[∊]/[∊]r |
| title_full | Generic character sheaves on groups over k[∊]/[∊]r |
| title_fullStr | Generic character sheaves on groups over k[∊]/[∊]r |
| title_full_unstemmed | Generic character sheaves on groups over k[∊]/[∊]r |
| title_short | Generic character sheaves on groups over k[∊]/[∊]r |
| title_sort | generic character sheaves on groups over k ∊ ∊ r |
| url | https://hdl.handle.net/1721.1/124911 |
| work_keys_str_mv | AT lusztiggeorge genericcharactersheavesongroupsoverkr |