Symmetric and alternating powers of Weil representations of finite symplectic groups

Robert M. Guralnick, Kay Magaard, Pham Huu Tiep

Type: Article

Publication Date: 2018-12-01

Citations: 9

DOI: https://doi.org/10.21915/bimas.2018405

Abstract

Motivated by an earlier result of N. Katz, we establish all possible equalities between symmetric squares, alternating squares, and tensor products of complex irreducible Weil characters of finite symplectic groups in odd characteristic.We also construct an infinite series of examples of irreducible symmetric cubes and alternating cubes of complex representations of finite groups.

Locations

Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES - View - PDF

Similar Works

Action	Title	Year	Authors
+	Totally orthogonal finite simple groups	2018	C. Ryan Vinroot
+	Totally orthogonal finite simple groups	2018	C. Ryan Vinroot
+	Two conjectures on the Weil representations of finite symplectic and unitary groups	2019	Gerhard Hiß Moritz Schröer
+	Weil Representations of Symplectic Groups Over Rings	2000	Gerald Cliff David McNeilly Fernando Szechtman
+	Weil representations of finite symplectic groups	1999	Fernando Szechtman
+	On the geometric Langlands conjecture for symplectic and odd orthogonal groups	2002	Sergey Lysenko
+	Arithmeticity of holomorphic cuspforms on Hermitian symmetric domains	2015	Dominic Lanphier Çetin Ürtiş
+	Weil representations of symplectic groups	2006	Gerald Cliff David McNeilly
+	Weil Representations of the Symplectic Group	1998	Fernando Szechtman
+	Real representations of finite symplectic groups over fields of characteristic two	2017	C. Ryan Vinroot
+	Real representations of finite symplectic groups over fields of characteristic two	2017	C. Ryan Vinroot
+	Powers in finite orthogonal and symplectic groups: A generating function approach	2024	Saikat Panja Anupam Singh
+	Arithmetic Aspects of the Theta Correspondence and Periods of Modular Forms	2007	Kartik Prasanna
+	Products of unipotent elements of index 2 in orthogonal and symplectic groups	2024	Clément de Seguins Pazzis
+	Apery Numbers and Modular Forms	1991	恒男石川
+	Hypergeometric sheaves and finite symplectic and unitary groups	2021	Nicholas M. Katz Pham Huu Tiep
+	Euler polynomials and alternating sums of powers of integers	2022	José L. Cereceda
+	Unipotent characters of the symplectic and odd orthogonal groups over a finite field	1981	G. Lusztig
+	Representations of Weil Groups	2006
+ PDF Chat	Arthur's multiplicity formula for certain inner forms of special orthogonal and symplectic groups	2018	Olivier Taïbi

Works That Cite This (9)

Action	Title	Year	Authors
+	Monodromy groups of certain Kloosterman and hypergeometric sheaves	2020	Nicholas M. Katz Pham Huu Tiep
+ PDF Chat	Moments of Weil representations of finite special unitary groups	2019	Nicholas M. Katz Pham Huu Tiep
+	Weil representations via abstract data and Heisenberg groups: A comparison	2019	James Cruickshank Luis Gutiérrez Frez Fernando Szechtman
+ PDF Chat	Unitary $t$-groups	2019	Eiichi Bannaĭ Gabriel Navarro Noelia Rizo Pham Huu Tiep
+ PDF Chat	On irreducible products of characters	2021	Gabriel Navarro Pham Huu Tiep
+	Rigid local systems and finite symplectic groups	2019	Nicholas M. Katz Pham Huu Tiep
+ PDF Chat	CHARACTER LEVELS AND CHARACTER BOUNDS	2020	Robert M. Guralnick Michael Larsen Pham Huu Tiep
+	Weil representations via abstract data and Heisenberg groups: a comparison	2019	James Cruickshank Luis Gutiérrez Frez Fernando Szechtman
+	Monodromy groups of Kloosterman and hypergeometric sheaves	2021	Nicholas M. Katz Pham Huu Tiep

Works Cited by This (24)

Action	Title	Year	Authors
+	Symplectic group lattices	1999	Rudolf Scharlau Pham Huu Tiep
+	Some Characterizations of the Weil Representations of the Symplectic and Unitary Groups	1997	Pham Huu Tiep Alexander E. Zalesskii
+	Almost irreducible tensor squares	1999	Gunter Malle
+	On the maximal subgroups of the finite classical groups	1984	Michael Aschbacher
+	Symplectic Groups, Symplectic Spreads, Codes, and Unimodular Lattices	1997	Rudolf Scharlau Pham Huu Tiep
+	Some Representations of Classical Groups	1975	Gary M. Seitz
+ PDF Chat	Irreducibility of tensor squares, symmetric squares and alternating squares	2002	Kay Magaard Gunter Malle Pham Huu Tiep
+	Real conjugacy classes in algebraic groups and finite groups of Lie type	2005	Pham Huu Tiep Alexandre Zalesski
+	Unipotent elements of finite groups of Lie type and realization fields of their complex representations	2003	Pham Huu Tiep Alexandre Zalesski
+	Even unimodular lattices associated with the Weil representation of the finite symplectic group	1989	Rod Gow