Jae-Hoon Kwon
A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators.
Wed, 07/07/2010 - 15:01 — SomNambulAuthors: Jae-Hoon Kwon
Subjects: Representation Theory
AbstractWe give a new bijective interpretation of the Cauchy identity for Schur
operators which is a commutation relation between two formal power series with
operator coefficients. We introduce a plactic algebra associated with the
Kashiwara's extremal weight crystals over the Kac-Moody algebra of type
$A_{+\infty}$, and construct a Knuth type correspondence preserving the plactic
relations.Crystal bases of modified quantum groups and RSK correspondence.
Tue, 02/09/2010 - 16:01 — SomNambulAuthors: Jae-Hoon Kwon
Subjects: Representation Theory
AbstractThe crystal base of the modified quantum group of type $A_{+\infty}$ is
realized as a set of integral bimatrices. It is obtained by describing
explicitly the tensor product of a highest weight crystal and a lowest weight
crystal, and then its limit using a tableaux model of extremal weight crystals.
This realization induces a bicrystal structure of the crystal base of the
modified quantum group and hence its Peter-Weyl type decomposition in a purely
combinatorial way generalizing the classical RSK correspondence.Crystal duality and Littlewood-Richardson rule of extremal weight crystals.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Jae-Hoon Kwon
Subjects: Quantum Algebra
AbstractWe consider a category of $\gl_\infty$-crystals, whose object is a disjoint
union of extremal weight crystals with bounded non-negative level and finite
multiplicity for each connected component. We show that it is a monoidal
category under tensor product of crystals and the associated Grothendieck ring
is anti-isomorphic to an Ore extension of the character ring of integrable
lowest $\gl_\infty$-modules with respect to derivations shifting the
fundamental weight characters.- Read more
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