scholarly journals Invariant Algebra and Cuspidal Representations of Finite Monoids

1999 ◽  
Vol 212 (2) ◽  
pp. 721-737 ◽  
Author(s):  
Mohan S Putcha
Keyword(s):  
Finite Monoids ◽  
Invariant Algebra ◽  
Cuspidal Representations

PARABOLIC SUBGROUPS AND CUSPIDAL REPRESENTATIONS OF FINITE MONOIDS

1991 ◽  
Vol 01 (01) ◽  
pp. 33-47 ◽  
Author(s):  
JAN OKNIŃSKI ◽  
MOHAN S. PUTCHA
Keyword(s):  
Inverse Semigroup ◽  
Finite Groups ◽  
Special Class ◽  
Semigroup Algebra ◽  
Parabolic Subgroups ◽  
Finite Monoids ◽  
Representations Of Finite Groups ◽  
Symmetric Inverse Semigroup ◽  
Complex Semigroup ◽  
Cuspidal Representations

This paper is mostly concerned with arbitrary finite monoids M with the complex semigroup algebra [Formula: see text] semisimple. Using the 1942 work of Clifford, we develop for these monoids a theory of cuspidal representations. Harish-Chandra's philosophy of cuspidal representations of finite groups can then be derived with an appropriate specialization. For [Formula: see text], we use Solomon's Hecke algebra to obtain a correspondence between the 'simple' representations of [Formula: see text] and the representations of the symmetric inverse semigroup. We also prove a semisimplicity theorem for a special class of finite monoids of the type which was earlier used by the authors to prove the semisimplicity of [Formula: see text].

scholarly journals On cuspidal representations of general linear groups over discrete valuation rings

2010 ◽  
Vol 175 (1) ◽  
pp. 391-420 ◽  
Author(s):  
Anne-Marie Aubert ◽  
Uri Onn ◽  
Amritanshu Prasad ◽  
Alexander Stasinski
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Cuspidal Representations

scholarly journals Burgess-like subconvexity for

2019 ◽  
Vol 155 (8) ◽  
pp. 1457-1499 ◽  
Author(s):  
Han Wu
Keyword(s):  
Eisenstein Series ◽  
Number Field ◽  
Main Tool ◽  
Previous Method ◽  
Triple Product ◽  
Extended Theory ◽  
Product Formulas ◽  
Cuspidal Representations

We generalize our previous method on the subconvexity problem for $\text{GL}_{2}\times \text{GL}_{1}$ with cuspidal representations to Eisenstein series, and deduce a Burgess-like subconvex bound for Hecke characters, that is, the bound $|L(1/2,\unicode[STIX]{x1D712})|\ll _{\mathbf{F},\unicode[STIX]{x1D716}}\mathbf{C}(\unicode[STIX]{x1D712})^{1/4-(1-2\unicode[STIX]{x1D703})/16+\unicode[STIX]{x1D716}}$ for varying Hecke characters $\unicode[STIX]{x1D712}$ over a number field $\mathbf{F}$ with analytic conductor $\mathbf{C}(\unicode[STIX]{x1D712})$ . As a main tool, we apply the extended theory of regularized integrals due to Zagier developed in a previous paper to obtain the relevant triple product formulas of Eisenstein series.

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