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 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 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

scholarly journals Quiver Hecke Algebras and 2-Lie Algebras

2012 ◽  
Vol 19 (02) ◽  
pp. 359-410 ◽  
Author(s):  
Raphaël Rouquier
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Hecke Algebras ◽  
Geometric Description ◽  
Monoidal Categories ◽  
Quiver Varieties ◽  
Basic Properties

We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting monoidal categories, which have a geometric description via quiver varieties, in certain cases. We present basic properties of 2-representations and describe simple 2-representations, via cyclotomic quiver Hecke algebras, and through microlocalized quiver varieties.

scholarly journals Two Maps on Affine Type $A$ Crystals and Hecke Algebras

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Nicolas Jacon
Keyword(s):  
Representation Theory ◽  
Quantum Groups ◽  
Fock Space ◽  
Hecke Algebras ◽  
Type A ◽  
Crystal Basis ◽  
Affine Type

We use the crystal isomorphisms of the Fock space to describe two maps on partitions and multipartitions which naturally appear in the crystal basis theory for quantum groups in affine type $A$ and in the representation theory of Hecke algebras of type $G(l,l,n)$. 

Sign in / Sign up

Export Citation Format

Share Document