q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations

将量子 affine 顶点代数的变形 $ϕ$-协调模与正交扭曲 $h$-Yangians 关联

Associating deformed $ϕ$-coordinated modules for the quantum affine vertex algebra with orthogonal twisted $h$-Yangians

本文通过引入变形 $ϕ$-协调模的概念，将量子 affine 顶点代数与正交扭曲 $h$-Yangians 关联，并展示其应用。

Full chains of twists for orthogonal algebras

We show that for some Hopf subalgebras in U_F(so(M)) nontrivially deformed by a twist F it is possible to find the nonlinear primitive copies. This enlarges the possibilities to construct chains of twists. For orthogonal algebra U(so(M)) we present a method to compose the full chains with carrier space as large as the Borel subalgebra B(so(M)). These chains can be used to construct the new deformed Yangians.

Q-pseudodifference Drinfeld-Sokolov reduction for algebra of complex size matrices

The q-deformed version of the Drinfeld-Sokolov reduction is extended to the case of the algebra of 'complex size matrices'; this construction generalizes earlier results of B.Khesin and F.Malikov on universal DS reduction and follows the pattern of recent studies of q-deformed DS reduction which were started by E.Frenkel, N.Reshetikhin and one of the authors.

Deformed and extended Galilei group Hopf algebras

The $\hatκ$-deformed extended Galilei Hopf group algebra, ${\rm Fun}_{\hatκ}(\tilde G_{(m)})$, is introduced. It provides an example of a cocycle bicrossproduct structure, and is shown to be the contraction limit of a pseudoextension of the $κ$-Poincaré group algebra. The possibility of obtaining another deformed extended Galilei groups is discussed, including one obtained from a non-standard Poincaré deformation.

Antiholomorphic representations for orthogonal and symplectic quantum groups

The coadjoint orbits for the series $B_l,\ C_l$ and $D_l$ are considered in the case when the base point is a multiple of a fundamental weight. A quantization of the big cell is suggested by means of introducing a $\ast$-algebra generated by holomorphic coordinate functions. Starting from this algebraic structure the irreducible representations of the deformed universal enveloping algebra are derived as acting in the vector space of polynomials in quantum coordinate functions.

On the dimensions of the oscillator algebras induced by orthogonal polynomials

There is a generalized oscillator algebra associated with every class of orthogonal polynomials $\{Ψ_n(x)\}_{n=0}^{\infty}$, on the real line, satisfying a three term recurrence relation $xΨ_n(x)=b_nΨ_{n+1}(x)+b_{n-1}Ψ_{n-1}(x), Ψ_0(x)=1, b_{-1}=0$. This note presents necessary and safficient conditions on $b_n$ for such algebras to be of finite dimension. As examples, we discuss the dimensions of oscillator algebras associated with Hermite, Legendre and Gegenbauer polynomials. In addition we shall also discuss the dimensions of some generalized deformed oscillator algebras. Some remarks on th…