Groups from Class 2 Algebras and the Weil Character
We investigate the behaviour of the Weil character of the symplectic group on restriction to subgroups arising from commutative nilpotent algebras of class 2. We give explicit descriptions of the decomposition of the Weil character when restricted to the unipotent radical of the stabilizer of a maxi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Aracne
2017-06-01
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| Series: | Advances in Group Theory and Applications |
| Subjects: | |
| Online Access: | http://www.advgrouptheory.com/journal/Volumes/3/C.A.%20Pallikaros,%20H.N.%20Ward%20-%20Groups%20from%20class%202%20algebras%20and%20the%20Weil%20character.pdf |
| _version_ | 1819153046722052096 |
|---|---|
| author | Christakis A. Pallikaros Harold N. Ward |
| author_facet | Christakis A. Pallikaros Harold N. Ward |
| author_sort | Christakis A. Pallikaros |
| collection | DOAJ |
| description | We investigate the behaviour of the Weil character of the symplectic group on restriction to subgroups arising from commutative nilpotent algebras of class 2. We give explicit descriptions of the decomposition of the Weil character when restricted to the unipotent radical of the stabilizer of a maximal totally isotropic subspace and to its centralizer. Moreover, we show how these decompositions can be used to obtain alternative proofs for certain results concerning quadratic forms or Gauss sums. |
| first_indexed | 2024-12-22T14:58:58Z |
| format | Article |
| id | doaj.art-abf4e5f2f5474da5a6a92b087763f132 |
| institution | Directory Open Access Journal |
| issn | 2499-1287 2499-1287 |
| language | English |
| last_indexed | 2024-12-22T14:58:58Z |
| publishDate | 2017-06-01 |
| publisher | Aracne |
| record_format | Article |
| series | Advances in Group Theory and Applications |
| spelling | doaj.art-abf4e5f2f5474da5a6a92b087763f1322022-12-21T18:22:09ZengAracneAdvances in Group Theory and Applications2499-12872499-12872017-06-0137596Groups from Class 2 Algebras and the Weil CharacterChristakis A. Pallikaros0Harold N. Ward1University of CyprusUniversity of VirginiaWe investigate the behaviour of the Weil character of the symplectic group on restriction to subgroups arising from commutative nilpotent algebras of class 2. We give explicit descriptions of the decomposition of the Weil character when restricted to the unipotent radical of the stabilizer of a maximal totally isotropic subspace and to its centralizer. Moreover, we show how these decompositions can be used to obtain alternative proofs for certain results concerning quadratic forms or Gauss sums.http://www.advgrouptheory.com/journal/Volumes/3/C.A.%20Pallikaros,%20H.N.%20Ward%20-%20Groups%20from%20class%202%20algebras%20and%20the%20Weil%20character.pdfWeil representationssymplectic groupquadratic form |
| spellingShingle | Christakis A. Pallikaros Harold N. Ward Groups from Class 2 Algebras and the Weil Character Advances in Group Theory and Applications Weil representations symplectic group quadratic form |
| title | Groups from Class 2 Algebras and the Weil Character |
| title_full | Groups from Class 2 Algebras and the Weil Character |
| title_fullStr | Groups from Class 2 Algebras and the Weil Character |
| title_full_unstemmed | Groups from Class 2 Algebras and the Weil Character |
| title_short | Groups from Class 2 Algebras and the Weil Character |
| title_sort | groups from class 2 algebras and the weil character |
| topic | Weil representations symplectic group quadratic form |
| url | http://www.advgrouptheory.com/journal/Volumes/3/C.A.%20Pallikaros,%20H.N.%20Ward%20-%20Groups%20from%20class%202%20algebras%20and%20the%20Weil%20character.pdf |
| work_keys_str_mv | AT christakisapallikaros groupsfromclass2algebrasandtheweilcharacter AT haroldnward groupsfromclass2algebrasandtheweilcharacter |