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 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 $G(l,l,n)$. 

scholarly journals Combinatorics of canonical bases revisited: type A

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Volker Genz ◽  
Gleb Koshevoy ◽  
Bea Schumann
Keyword(s):  
Type A ◽  
Canonical Bases

scholarly journals OCNEANU'S TRACE AND STARKEY'S RULE

2003 ◽  
Vol 12 (07) ◽  
pp. 899-904 ◽  
Author(s):  
MEINOLF GECK ◽  
NICOLAS JACON
Keyword(s):  
Simple Proof ◽  
Hecke Algebras ◽  
Jones Polynomial ◽  
Main Tool ◽  
Type A ◽  
Character Tables ◽  
Special Case ◽  
Knots And Links

We give a new simple proof for the weights of Ocneanu's trace on Iwahori–Hecke algebras of type A. This trace is used in the construction of the HOMFLYPT-polynomial of knots and links (which includes the famous Jones polynomial as a special case). Our main tool is Starkey's rule concerning the character tables of Iwahori–Hecke algebras of type A.

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