Self-extensions for finite symplectic groups via algebraic groups

2006 ◽  
pp. 173-184
Author(s):  
Cornelius Pillen
Keyword(s):  
Algebraic Groups ◽  
Symplectic Groups ◽  
Finite Symplectic Groups

scholarly journals Real Representations of Finite Symplectic Groups over Fields of Characteristic Two

2018 ◽  
Vol 2020 (5) ◽  
pp. 1281-1299 ◽  
Author(s):  
C Ryan Vinroot
Keyword(s):  
Irreducible Representation ◽  
Generating Function ◽  
Prime Power ◽  
Symplectic Groups ◽  
Real Numbers ◽  
The Real ◽  
Characteristic Two ◽  
Finite Symplectic Groups

Abstract We prove that when q is a power of 2 every complex irreducible representation of $\textrm{Sp}\big (2n, \mathbb{F}_{q}\big )$ may be defined over the real numbers, that is, all Frobenius–Schur indicators are 1. We also obtain a generating function for the sum of the degrees of the unipotent characters of $\textrm{Sp}\big(2n, \mathbb{F}_{q}\big )$, or of $\textrm{SO}\big(2n+1,\mathbb{F}_{q}\big )$, for any prime power q.

scholarly journals Rigid local systems and finite symplectic groups

2019 ◽  
Vol 59 ◽  
pp. 134-174 ◽  
Author(s):  
Nicholas M. Katz ◽  
Pham Huu Tiep
Keyword(s):  
Symplectic Groups ◽  
Local Systems ◽  
Finite Symplectic Groups

scholarly journals Restricting Unipotent Characters in Finite Symplectic Groups

2011 ◽  
Vol 39 (3) ◽  
pp. 1104-1130 ◽  
Author(s):  
Jianbei An ◽  
Gerhard Hiss
Keyword(s):  
Symplectic Groups ◽  
Finite Symplectic Groups

THE INDUCTIVE BLOCKWISE ALPERIN WEIGHT CONDITION FOR TYPE AND THE PRIME

2020 ◽  
pp. 1-20
Author(s):  
ZHICHENG FENG ◽  
GUNTER MALLE
Keyword(s):  
Simple Groups ◽  
Main Step ◽  
Symplectic Groups ◽  
Jordan Decomposition ◽  
Important Ingredient ◽  
Weight Condition ◽  
Brauer Characters ◽  
Groups Of Lie Type ◽  
Finite Symplectic Groups

Abstract We establish the inductive blockwise Alperin weight condition for simple groups of Lie type $\mathsf C$ and the bad prime $2$ . As a main step, we derive a labelling set for the irreducible $2$ -Brauer characters of the finite symplectic groups $\operatorname {Sp}_{2n}(q)$ (with odd q), together with the action of automorphisms. As a further important ingredient, we prove a Jordan decomposition for weights.

RESTRICTIONS OF SOME REPRESENTATIONS OF THE SYMPLECTIC GROUP TO SUBGROUPS OF TYPE A1

2007 ◽  
Vol 06 (04) ◽  
pp. 697-701
Author(s):  
ANNA A. OSINOVSKAYA
Keyword(s):  
Algebraic Group ◽  
Symplectic Group ◽  
Algebraic Groups ◽  
Type A ◽  
Irreducible Representations ◽  
Symplectic Groups ◽  
Inductive System ◽  
Highest Weight ◽  
Composition Factors

Restrictions of modular irreducible representations of the symplectic algebraic group to naturally embedded long subgroups of type A1 are studied. Let ω = m1ω1 + ⋯ + mnωn be the highest weight of such representation. The composition factors of such restrictions are determined in the case of m1 + ⋯ + mn + 3 ≤ p < mn-1 + 2mn + 3 that completes the description of restrictions of classical algebraic groups to naturally embedded A1-subgroups and gives an example of a new inductive system of representations of symplectic groups that has no analogues in characteristic 0.

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