Involutive automorphism of symmetric groups

2017 ◽  
Vol 46 (6) ◽  
pp. 2693-2695
Author(s):  
Hou-Yi Chen
Keyword(s):  
Symmetric Groups ◽  
Involutive Automorphism

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

scholarly journals Irreducible restrictions of representations of symmetric groups in small characteristics: reduction theorems

2018 ◽  
Vol 293 (1-2) ◽  
pp. 677-723 ◽  
Author(s):  
Alexander Kleshchev ◽  
Lucia Morotti ◽  
Pham Huu Tiep
Keyword(s):  
Symmetric Groups

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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