2026-09-18T18:07:01Zhttps://dspace.mit.edu/server/oai/request

oai:dspace.mit.edu:1721.1/1173132026-06-16T18:17:33Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022

George Lusztig. Kim, Dongkwan, Sc.D. Massachusetts Institute of Technology Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics 2018-08-08T19:48:50Z 2018-08-08T19:48:50Z 2018 2018 http://hdl.handle.net/1721.1/117313 1045072068 Thesis: Sc. D., Massachusetts Institute of Technology, Department of Mathematics, 2018. Cataloged from PDF version of thesis. Includes bibliographical references (pages 133-136). 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. by Dongkwan Kim. Sc.D. 136 pages eng Massachusetts Institute of Technology 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 Mathematics. On total Springer representations Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="7de060c5-aec3-4499-b320-290c4401349e"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>On total Springer representations</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2018</PublicationDate> <Authors> <Author> <DisplayName>Kim, Dongkwan, Sc.D. Massachusetts Institute of Technology</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Mathematics.</Keyword> <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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>