scholarly journals Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups

2009 ◽  
Vol 119 (1) ◽  
pp. 81-100 ◽  
Author(s):  
S. S. Kannan ◽  
Sardar Pranab
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Homogeneous Spaces ◽  
Symmetric Groups ◽  
General Linear ◽  
Standard Representation

Ext spaces for general linear and symmetric groups

1991 ◽  
Vol 119 (3-4) ◽  
pp. 301-310 ◽  
Author(s):  
Stuart Martin
Keyword(s):  
Symmetric Group ◽  
Linear Group ◽  
General Linear Group ◽  
Symmetric Groups ◽  
General Linear ◽  
Simple Modules

SynopsisWe consider the links between Ext1 groups of simple modules for the symmetric group, and Ext1 of simple modules for the general linear group.

Representations induced from the Zelevinsky segment and discrete series in the half-integral case

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Discrete Series ◽  
Series Representation ◽  
General Linear ◽  
Composition Series ◽  
Induced Representations ◽  
Discrete Series Representation

AbstractLet {G_{n}} denote either the group {\mathrm{SO}(2n+1,F)} or {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form {\langle\Delta\rangle\rtimes\sigma}, where {\langle\Delta\rangle} denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of {G_{n}}. We determine the composition series of {\langle\Delta\rangle\rtimes\sigma} in the case when {\Delta=[\nu^{a}\rho,\nu^{b}\rho]} where a is half-integral.

scholarly journals Triple factorisations of the general linear group and their associated geometries

2015 ◽  
Vol 469 ◽  
pp. 169-203 ◽  
Author(s):  
Seyed Hassan Alavi ◽  
John Bamberg ◽  
Cheryl E. Praeger
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
General Linear
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