scholarly journals Spinoriality of orthogonal representations of reductive groups

2020 ◽  
Vol 24 (15) ◽  
pp. 435-469
Author(s):  
Rohit Joshi ◽  
Steven Spallone
Keyword(s):  
Reductive Groups ◽  
Orthogonal Representations

scholarly journals STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

2021 ◽  
pp. 1-48
Author(s):  
Federico Scavia
Keyword(s):  
Finite Groups ◽  
Reductive Groups ◽  
Orthogonal Groups ◽  
De Rham Cohomology ◽  
Algebraic Stacks ◽  
Steenrod Operations ◽  
De Rham

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

Symplectic slices for actions of reductive groups

2006 ◽  
Vol 197 (2) ◽  
pp. 213-224
Author(s):  
I V Losev
Keyword(s):  
Reductive Groups

scholarly journals Alvis–Curtis duality for representations of reductive groups with Frobenius maps

2020 ◽  
Vol 32 (5) ◽  
pp. 1289-1296
Author(s):  
Junbin Dong
Keyword(s):  
Irreducible Representations ◽  
Reductive Groups ◽  
Infinite Type ◽  
Abstract Representations

AbstractWe generalize the Alvis–Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis–Curtis duality of infinite type, which we define in this paper, also interchanges the irreducible representations in the principal representation category.

Symmetries of double ratios and an equation for Möbius structures

2021 ◽  
Vol 33 (1) ◽  
pp. 47-56
Author(s):  
S. Buyalo
Keyword(s):  
Symmetric Groups ◽  
Content Type ◽  
Irreducible Components ◽  
Orthogonal Representations

Orthogonal representations η n : S n ↷ R N \eta _n\colon S_n\curvearrowright \mathbb {R}^N of the symmetric groups S n S_n , n ≥ 4 n\ge 4 , with N = n ! / 8 N=n!/8 , emerging from symmetries of double ratios are treated. For n = 5 n=5 , the representation η 5 \eta _5 is decomposed into irreducible components and it is shown that a certain component yields a solution of the equations that describe the Möbius structures in the class of sub-Möbius structures. In this sense, a condition determining the Möbius structures is implicit already in symmetries of double ratios.

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