Computing the Lusztig-Vogan bijection
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2018
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| Online Access: | http://hdl.handle.net/1721.1/113549 |
| _version_ | 1811082994636554240 |
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| author | Rush, David B., Ph. D. Massachusetts Institute of Technology |
| author2 | David A. Vogan Jr. |
| author_facet | David A. Vogan Jr. Rush, David B., Ph. D. Massachusetts Institute of Technology |
| author_sort | Rush, David B., Ph. D. Massachusetts Institute of Technology |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017. |
| first_indexed | 2024-09-23T12:17:02Z |
| format | Thesis |
| id | mit-1721.1/113549 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:17:02Z |
| publishDate | 2018 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1135492019-04-12T23:11:54Z Computing the Lusztig-Vogan bijection Rush, David B., Ph. D. Massachusetts Institute of Technology David A. Vogan Jr. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017. Cataloged from PDF version of thesis. Includes bibliographical references (pages 129-130). Let G be a connected complex reductive algebraic group with Lie algebra g. The Lusztig-Vogan bijection relates two bases for the bounded derived category of G-equivariant coherent sheaves on the nilpotent cone 11 of g. One basis is indexed by ..., the set of dominant weights of G, and the other by [Omega], the set of pairs ... consisting of a nilpotent orbit ... and an irreducible G-equivariant vector bundle ... The existence of the Lusztig-Vogan bijection ... was proven by Bezrukavnikov, and an algorithm computing [gamma] in type A was given by Achar. Herein we present a combinatorial description of [gamma] in type A that subsumes and dramatically simplifies Achar's algorithm. by David B Rush. Ph. D. 2018-02-08T16:28:42Z 2018-02-08T16:28:42Z 2017 2017 Thesis http://hdl.handle.net/1721.1/113549 1020252308 eng MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 130 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Rush, David B., Ph. D. Massachusetts Institute of Technology Computing the Lusztig-Vogan bijection |
| title | Computing the Lusztig-Vogan bijection |
| title_full | Computing the Lusztig-Vogan bijection |
| title_fullStr | Computing the Lusztig-Vogan bijection |
| title_full_unstemmed | Computing the Lusztig-Vogan bijection |
| title_short | Computing the Lusztig-Vogan bijection |
| title_sort | computing the lusztig vogan bijection |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/113549 |
| work_keys_str_mv | AT rushdavidbphdmassachusettsinstituteoftechnology computingthelusztigvoganbijection |