Related papers: On the relation between $U_q(\widehat{sl(2)})$ ver…
In this paper, we describe a certain kind of $q$-connections on a projective line, namely $Z$-twisted $(G,q)$-opers with regular singularities using the language of generalized minors. In part one arXiv:2002.07344 we explored the…
A level-one representation of the quantum affine superalgebra $\U_q(\hat{\frak{sl}}(M+1|N+1))$ and vertex operators associated with the fundamental representations are constructed in terms of free bosonic fields. Character formulas of…
Width of molecular-type $Q\bar{Q}q\bar{q}$ hadronic states is discussed. It depends on the quantum numbers of the state and on the details of the long-range mechanism ensuring the bindedness of a molecule. Specific cases when the width is…
We construct a vertex representation for the quantum toroidal algebra through the quantum general linear algebra. Using a new realization of the quantum general linear algebra we construct vertex operators for root vectors on the basic…
We prove that, for the quon algebra, which interpolates between the Bose and Fermi statistics and depends on a free parameter q,it is possible to build an su(2) irreducible representation. One of the consequences of this fact is that the…
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…
Assuming the existence of the L-operators, we study the Hopf algebroid structure of U_{q,p}(B_N^{(1)}). As an application, we derive the type I and II vertex operators, which intertwine the U_{q,p}(B_N^{(1)})-modules of generic level, by…
In this paper we consider how the following three objects are related: (i) the dual polar graphs; (ii) the quantum algebra U_q(sl_2); (iii) the Leonard systems of dual q-Krawtchouk type. For convenience we first describe how (ii) and (iii)…
We determine the exchange relations of the level-one q-vertex operators of the quantum affine superalgebra $U_q[\hat{gl(N|N)}]$. We study in details the level-one irreducible highest weight representations of $U_q[\hat{gl(2|2)}]$, and…
A Fock representation of the quantum affine algebra $U_q(\widehat{\sl}_2)$ is constructed by three bosonic fields for an arbitrary level with the help of the Drinfeld realization.
Definition of Dirac operators on the quantum group $SU_{q}(2)$ and the quantum sphere $S^{2}_{q \mu}$ are discussed. In both cases similar $SU_{q}(2)$-invariant form is obtained. It is connected with corresponding Laplace operators.
We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra.…
Linear operators $R$ are introduced on tensor products of evaluation modules of $U'_q\bigl(\widehat{sl}(2)\bigr)$ obtained from the complementary and strange series representations. The operators $R$ satisfy the intertwining condition on…
We establish an isomorphism between the space of logarithmic intertwining operators among suitable generalized modules for a vertex operator algebra and the space of homomorphisms between suitable modules for a generalization of Zhu's…
We show that the multi-species higher spin stochastic vertex model, also called the U_q(A_n^{(1)}) vertex model, satisfies a duality where the indicator function has the form {\eta^x_{[1,n]} \geq \xi^x_{[1,n]} }. In other words, for every…
In this paper, we establish the connection between the quantized W-algebra of ${\frak sl}(2,1)$ and quantum parafermions of $U_q(\hat {\frak sl}(2))$ that a shifted product of the two quantum parafermions of $U_q(\hat {\frak sl}(2))$…
Using matrix corepresentations on SL_q(N) and SU_q(N) we derive a Haar state on SU_q(N) which is nearly identical to that on SU_q(2). This allows us to create an orthonormal basis for the vector space of coordinate functions on SU_q(N).
In this paper we consider a very general U(1)-invariant field theory such that a field operator commutes with its adjoint, what corresponds to a theory of a charged bosonic particle. We show that from such an invariance follows the…
The three point correlation functions with twist fields are determined for bosonic $Z_N$ orbifolds. Both the choice of the modular background (compatible with the twist) and of the (higher) twisted sectors involved are fully general. We…
A certain class of unitary representations of U_q(sl(2,R)) has the property of being simultanenously a representation of U_{tilde{q}}(sl(2,R)) for a particular choice of tilde{q}(q). Faddeev has proposed to unify the quantum groups…