scholarly journals The Atiyah conjecture for the Hecke algebra of the infinite dihedral group

2014 ◽  
Vol 8 (4) ◽  
pp. 1161-1194 ◽  
Author(s):  
Boris Okun ◽  
Richard Scott
Keyword(s):  
Dihedral Group ◽  
Hecke Algebra ◽  
Atiyah Conjecture

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 Some characterizatsion of coprime graph of dihedral group D 2n

2021 ◽  
Vol 1722 ◽  
pp. 012051
Author(s):  
A G Syarifudin ◽  
Nurhabibah ◽  
D P Malik ◽  
I G A W Wardhana
Keyword(s):  
Dihedral Group ◽  
Group D

scholarly journals Three-state quantum walk on the Cayley Graph of the Dihedral Group

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Ying Liu ◽  
Jia-bin Yuan ◽  
Wen-jing Dai ◽  
Dan Li
Keyword(s):  
Cayley Graph ◽  
Dihedral Group ◽  
Quantum Walk

scholarly journals A note on central group extensions

1973 ◽  
Vol 15 (4) ◽  
pp. 428-429 ◽  
Author(s):  
G. J. Hauptfleisch
Keyword(s):  
Abelian Group ◽  
Homomorphic Image ◽  
Free Group ◽  
Central Extension ◽  
Dihedral Group ◽  
Group Extension ◽  
Central Group ◽  
Group Extensions

If A, B, H, K are abelian group and φ: A → H and ψ: B → K are epimorphisms, then a given central group extension G of H by K is not necessarily a homomorphic image of a group extension of A by B. Take for instance A = Z(2), B = Z ⊕ Z, H = Z(2), K = V4 (Klein's fourgroup). Then the dihedral group D8 is a central extension of H by K but it is not a homomorphic image of Z ⊕ Z ⊕ Z(2), the only group extension of A by the free group B.

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 Strong duality for metacyclic groups

2002 ◽  
Vol 73 (3) ◽  
pp. 377-392 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó
Keyword(s):  
Finite Group ◽  
Dihedral Group ◽  
Strong Duality ◽  
Sylow Subgroups ◽  
Metacyclic Groups ◽  
Group D

AbstractDavey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).

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
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