Gelfand–Tsetlin bases of representations for super Yangian and quantum affine superalgebra

Representations of super Yangian

We present in detail the classification of the finite dimensional irreducible representations of the super Yangian associated with the Lie superalgebra gl(1|1). 1 Introduction Many new algebraic structures were discovered in the study of soluble models in statistical mechanics and quantum field theory. Amongst them the quantum groups[1][2] and Yangians[3] are particularly interesting. The forme...

Crystal Bases for the Quantum Superalgebra

Yangian of the Queer Lie Superalgebra

Consider the complex matrix Lie superalgebra glN|N with the standard generators Eij where i, j = ±1 , . . . ,±N . Define an involutory automorphism η of glN|N by η (Eij) = E−i,−j . The twisted polynomial current Lie superalgebra g = {X(u) ∈ glN|N [u] : η (X(u)) = X(−u) } has a natural Lie co-superalgebra structure. We quantise the universal enveloping algebra U(g) as a co-Poisson Hopf superalge...

Crystal Bases for the Quantum Superalgebra Uq(gl(m,n))

Fractional Spin through Quantum Affine Algebra Â(n) and quantum affine superalgebra Â(n,m)

Using the splitting of a Q-deformed boson, in the Q → q = e 2πi k limit, the fractional decomposition of the quantum affine algebra Â(n) and the quantum affine superalgebra Â(n,m) are found. This decomposition is based on the oscillator representation and can be related to the fractional supersymmetry and k-fermionic spin. We establish also the equivalence between the quantum affine algebra Â(n...