REPRESENTATIONS OF THE HECKE ALGEBRA FOR GL4(q)

2005 ◽  
Vol 04 (06) ◽  
pp. 631-644
Author(s):  
KENICHI SHINODA ◽  
ILKNUR TULUNAY
Keyword(s):  
Hecke Algebra ◽  
Standard Basis

In this article, we explicitly calculated the values of the representations of the Hecke algebra [Formula: see text], associated with a Gelfand–Graev character of GL 4(q), at some of the standard basis elements.

scholarly journals Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 779
Author(s):  
Charles F. Dunkl
Keyword(s):  
Preceding Paper ◽  
Hecke Algebra ◽  
Type A ◽  
Macdonald Polynomials ◽  
Special Points ◽  
Two Parameters

In a preceding paper the theory of nonsymmetric Macdonald polynomials taking values in modules of the Hecke algebra of type A (Dunkl and Luque SLC 2012) was applied to such modules consisting of polynomials in anti-commuting variables, to define nonsymmetric Macdonald superpolynomials. These polynomials depend on two parameters q,t and are defined by means of a Yang–Baxter graph. The present paper determines the values of a subclass of the polynomials at the special points 1,t,t2,… or 1,t−1,t−2,…. The arguments use induction on the degree and computations with products of generators of the Hecke algebra. The resulting formulas involve q,t-hook products. Evaluations are also found for Macdonald superpolynomials having restricted symmetry and antisymmetry properties.

scholarly journals Hecke Algebra Actions on the Coinvariant Algebra

2000 ◽  
Vol 233 (2) ◽  
pp. 594-613 ◽  
Author(s):  
Ron M. Adin ◽  
Alexander Postnikov ◽  
Yuval Roichman
Keyword(s):  
Hecke Algebra ◽  
Coinvariant Algebra

FORMATION OF EXPERIMENTAL AND METHODICAL BASIS TO ESTIMATE STRENGTH CORRESPONDENCE OF DOMESTIC PASSENGER CAR BODIES TO EUROPEAN STANDARD BASIS

2021 ◽  
Vol 2021 (8) ◽  
pp. 67-76
Author(s):  
Sergey Korshunov ◽  
Aleksandr Skachkov ◽  
Sergey Samoshkin ◽  
Aleksandr Smirnov ◽  
Dmitriy Goncharov
Keyword(s):  
International Markets ◽  
The Body ◽  
Standard Basis ◽  
Rolling Stock ◽  
European Standard ◽  
Static Tests ◽  
Railway Infrastructure ◽  
Methodical Basis ◽  
Equipment Development ◽  
European Standards

The development of the international trade and the entrance of domestic car manufacturers into international markets required bench equipment development for tests in accordance with the requirements of the European standards. In this connection the purpose of this work is to develop an experimental and methodical basis for the estimation of the strength correspondence of export railway produce to the European standard basis. In the work there is shown a description of the bench developed for static tests of rolling stock for loads corresponding to the European standard basis. In the requirements mentioned there is used a more extended list of loads and combination of efforts and the necessity in the application of longitudinal loads to the elements of the end wall in three levels should be particularly emphasized. On the test bench there are carried out static tests of the car of model 61-4514 for Egyptian national railways and the body of the motor-rail car of model 2853 for the railway infrastructure of Serbia.

scholarly journals A quantum probabilistic approach to Hecke algebras for 𝔭-adic PGL2

2018 ◽  
Vol 21 (03) ◽  
pp. 1850015
Author(s):  
Takehiro Hasegawa ◽  
Hayato Saigo ◽  
Seiken Saito ◽  
Shingo Sugiyama
Keyword(s):  
Inversion Formula ◽  
Probabilistic Approach ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Quantum Probability ◽  
Probabilistic Interpretation ◽  
Fourier Inversion ◽  
Fourier Inversion Formula ◽  
The Subject

The subject of the present paper is an application of quantum probability to [Formula: see text]-adic objects. We give a quantum-probabilistic interpretation of the spherical Hecke algebra for [Formula: see text], where [Formula: see text] is a [Formula: see text]-adic field. As a byproduct, we obtain a new proof of the Fourier inversion formula for [Formula: see text].

The Hecke Algebra and Kazhdan–Lusztig Polynomials

2020 ◽  
pp. 39-58
Author(s):  
Ben Elias ◽  
Shotaro Makisumi ◽  
Ulrich Thiel ◽  
Geordie Williamson
Keyword(s):  
Hecke Algebra ◽  
Lusztig Polynomials
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