MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Theses - Dept. of Mathematics
  • Mathematics - Ph.D. / Sc.D.
  • View Item
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Theses - Dept. of Mathematics
  • Mathematics - Ph.D. / Sc.D.
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

On total Springer representations

Author(s)
Kim, Dongkwan, Sc.D. Massachusetts Institute of Technology
Thumbnail
DownloadFull printable version (5.985Mb)
Other Contributors
Massachusetts Institute of Technology. Department of Mathematics.
Advisor
George Lusztig.
Terms of use
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
Metadata
Show full item record
Abstract
This thesis studies the alternating sum of cohomology groups of a Springer fiber (in characteristic 0), called a total Springer representation, as a representation of both the Weyl group and the stabilizer of the corresponding nilpotent element. For classical types, we present explicit formulas for the decomposition of total Springer representations into irreducible ones of the corresponding Weyl group using Kostka-Foulkes polynomials. Also, the character value at any element contained in the maximal parabolic subgroup(s) of type A is explicitly given in terms of Green polynomials. As a result, closed formulas for the Euler characteristic of Springer fibers are deduced. Our proof relies on analysis of geometry of Springer fibers and combinatorics of symmetric functions. Moreover, we provide formulas for the character value of a total Springer representation at any element in the stabilizer of the corresponding nilpotent element. For exceptional types, the character values of total Springer representations are completely known. Here, we only describe the decomposition of such representations into irreducible ones of stabilizers of corresponding nilpotent elements.
Description
Thesis: Sc. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 133-136).
 
Date issued
2018
URI
http://hdl.handle.net/1721.1/117313
Department
Massachusetts Institute of Technology. Department of Mathematics.
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

Collections
  • Mathematics - Ph.D. / Sc.D.
  • Mathematics - Ph.D. / Sc.D.

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.