scholarly journals ON REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS

2011 ◽  
Vol 26 (11) ◽  
pp. 795-803 ◽  
Author(s):  
O. V. OGIEVETSKY ◽  
L. POULAIN D'ANDECY
Keyword(s):  
Representation Theory ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Cyclotomic Hecke Algebra ◽  
Cyclotomic Hecke Algebras

An approach, based on Jucys–Murphy elements, to the representation theory of cyclotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra) of the set of the Jucys–Murphy elements is established. A basis of the cyclotomic Hecke algebra is suggested; this basis is used to establish the flatness of the deformation without using the representation theory.

scholarly journals A note on the representation theory of the Hecke algebra of type F4

1997 ◽  
Vol 39 (1) ◽  
pp. 43-50 ◽  
Author(s):  
C. A. Pallikaros
Keyword(s):  
Representation Theory ◽  
Hecke Algebras ◽  
Hecke Algebra

In [4] Dipper and James investigated the representation theory of Hecke algebras of type Bn, H(Bn). Using the results in [4] and exploiting the fact that the Hecke algebra of type F4, denoted by H(W), contains two copies of H(B3) certain right ideals of H(W) will be constructed in this paper. These right ideals will be proved to be irreducible on the assumption that H(W) is semisimple.

scholarly journals Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r)

2010 ◽  
Vol 197 ◽  
pp. 175-212
Author(s):  
Maria Chlouveraki
Keyword(s):  
Infinite Series ◽  
Hecke Algebras ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Cyclotomic Hecke Algebras

The Rouquier blocks of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the families of characters defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite seriesG(de, e, r), thus completing their calculation for all complex reflection groups.

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].

Iwahori-Hecke Algebras and their Representation Theory

2002 ◽  
Author(s):  
Ivan Cherednik ◽  
Yavor Markov ◽  
Roger Howe ◽  
George Lusztig
Keyword(s):  
Representation Theory ◽  
Hecke Algebras
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