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An approach, based on Jucys–Murphy elements, to the representation theory of cy-clotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra)of the set of the Jucys–Murphy ele...
Lowest weight representations of super Schrodinger algebras in low dimensional spacetime
super Schrodinger algebras dimensional spacetime
2010/11/24
We investigate the lowest weight representations of the super Schrodinger algebras introduced by Duval and Horvathy. This is done by the same procedure as the semisimple Lie algebras. Namely, all sin...
Integrable representations of involutive algebras and Ore localization
Integrable representations involutive algebras Ore localization
2011/2/24
LetAbe a unital algebra equippedwith an involution (·)†, and suppose that the multiplicative set S ⊆ A generated by the elements of the form 1 + a†a satisfies the Ore condition.
We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known propertie...
Graphical representations of Ising and Potts models
Graphical representations Ising and Potts models
2010/11/18
We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz a...
Modular branching rules for projective representations of symmetric groups and lowering operators for the supergroup Q(n)
projective representations symmetric groups lowering operators the supergroup Q(n)
2010/11/9
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which...
Representations of monomial algebras have poly-exponential complexities
monomial algebras poly-exponential complexities
2010/11/22
We use directed graphs called "syzygy quivers" to study the asymptotic growth rates of the dimensions of the syzygies of representations of finite dimensional algebras. For any finitely generated rep...
Supports of representations of the rational Cherednik algebra of type A
representations rational Cherednik algebra of type A
2011/1/21
We first consider the rational Cherednik algebra corresponding to the action of a finite group on a complex variety, as defined by Etingof. We define a category of representations of this algebra whic...
Representations of the Temperley-Lieb Algebra via a New Inner Product on Half-Diagrams
Representations of the Temperley-Lieb Algebra New Inner Product Half-Diagrams
2011/1/17
The Temperley-Lieb algebra is an algebra given by generators and relations which arose in a problem in statistical mechanics considered by Temper-ley and Lieb [8]. Since then the algebra has been used...
SU(2) Representations of The Groups of Integer Tangles
Representation space knot group quaternions
2010/2/26
In this work we classify the irreducible SU(2) representations of P1(S3\backslash kn) where kn is an integer n tangle and as a result we have proved the following theorem: Let n be an odd integer then...
The kernel of Fock representations of Wick algebras with braided operator of coefficients
Fock representations algebras braided operator of coefficients
2010/11/1
It is shown that the kernel of the Fock representation of a certain Wick algebra with braided operator of coefficients T, || T ||<= 1, coincides with the largest quadratic Wick ideal. Improved condit...