Crystal of affine type Aˆℓ−1 and Hecke algebras at a primitive 2ℓth root of unity

2021 ◽  
Author(s):  
Huang Lin ◽  
Jun Hu
Keyword(s):  
Hecke Algebras ◽  
Root Of Unity ◽  
Affine Type

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 $G(l,l,n)$. 

UNITARY BRAID REPRESENTATIONS

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 985-1006
Author(s):  
HANS WENZL
Keyword(s):  
Quantum Groups ◽  
Braid Group ◽  
Deformation Parameter ◽  
Hecke Algebras ◽  
Tensor Products ◽  
Roots Of Unity ◽  
Von Neumann ◽  
Root Of Unity ◽  
Brauer Algebras ◽  
Original Motivation

The original motivation for studying unitarizable representations of the braid group was to construct interesting examples of subfactors of II1 von Neumann factors. This is possible for representations factoring through Hecke algebras or q-Brauer algebras only if the deformation parameter is a root of unity. Information gained from this work can be applied to studying tensor products of representations of quantum groups at roots of unity and invariants of 3-manifolds.

ON SCHUR-WEYL DUALITY, An HECKE ALGEBRAS AND QUANTUM sl(N) ON $\otimes^{n+1}{\mathbb C}^N$

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 645-673 ◽  
Author(s):  
PAUL PURDON MARTIN
Keyword(s):  
Hecke Algebras ◽  
Hecke Algebra ◽  
Model Representation ◽  
Complete Analysis ◽  
Vertex Model ◽  
Algebraic Structures ◽  
Root Of Unity ◽  
Weyl Duality

We prove that an N-state vertex model representation of the An Hecke algebra quotient NHn(q) is faithful for all q. We use the result to examine the indecomposable content of these representations, and hence the structure of the centraliser algebra, which is generically a quotient of Uqsl(N), at q a root of unity. We achieve a complete analysis in the case N=2, finding a number of Morita self-dual algebraic structures.

scholarly journals Uglov Bipartitions and Extended Young Diagrams

10.37236/8559 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Nicolas Jacon
Keyword(s):  
Hecke Algebras ◽  
Type A ◽  
Young Diagrams ◽  
Canonical Bases ◽  
Arbitrary Characteristic ◽  
Affine Type

We study the class of Uglov bipartitions and prove a generalization of a conjecture by Dipper, James and Murphy. We give two consequences concerning the computation of canonical bases in affine type $A$ and the description of decomposition matrices for Hecke algebras of type $B_n$ in arbitrary characteristic.

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

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