arXiv subjects

Slaven Kozic

Publications and source records attributed to Slaven Kozic.

5 recordsLinked to original sources

arXiv2017

Vertex operators and principal subspaces of level one for $U_q (\widehat{\mathfrak{sl}}_2)$

We consider two different methods of associating vertex algebraic structures with the level $1$ principal subspaces for $U_q (\widehat{\mathfrak{sl}}_2)$. In the first approach, we introduce certain commutative operators and study the corresponding vertex algebra and its module. We find combinatorial bases for these objects and show that they coincide with the principal subspace bases found by B. L. Feigin and A. V. Stoyanovsky. In the second approach, we introduce the, so-called nonlocal $\underline{\mathsf{q}}$-vertex algebras, investigate their properties and construct the nonlocal $\underline{\mathsf{q}}$-vertex algebra and its module, generated by Frenkel-Jing operator and Koyama's operator respectively. By finding the combinatorial bases of their suitably defined subspaces, we establish a connection with the sum sides of the Rogers-Ramanujan identities. Finally, we discuss further applications to quantum quasi-particle relations.

math.QA↗

arXiv2016

Higher level vertex operators for $U_q (\hat{\mathfrak{sl}}_2)$

We study graded nonlocal $\underline{\mathsf{q}}$-vertex algebras and we prove that they can be generated by certain sets of vertex operators. As an application, we consider the family of graded nonlocal $\underline{\mathsf{q}}$-vertex algebras $V_{c,1}$, $c\geq 1$, associated with the principal subspaces $W(cΛ_0)$ of the integrable highest weight $U_q (\hat{\mathfrak{sl}}_2)$-modules $L(cΛ_0)$. Using quantum integrability, we derive combinatorial bases for $V_{c,1}$ and compute the corresponding character formulae.

math.QA↗

arXiv2015

A note on the zeroth products of Frenkel-Jing operators

Quantum vertex algebra theory, developed by H.-S. Li, allows us to apply zeroth products of Frenkel-Jing operators, corresponding to Drinfeld realization of $U_q (\widehat{\mathfrak{sl}}_{n+1})$, on the extension of Koyama vertex operators. As a result, we obtain an infinite-dimensional space and describe its structure as a module for the associative algebra $U_q (\mathfrak{sl}_{n+1})_z$, a certain quantum analogue of $U(\mathfrak{sl}_{n+1})$ which we introduce in this paper.

math.QA↗

arXiv2014

Quasi-particles in the principal picture of $\widehat{\mathfrak{sl}}_{2}$ and Rogers-Ramanujan-type identities

In their seminal work J. Lepowsky and R. L. Wilson gave a vertex-operator theoretic interpretation of Gordon-Andrews-Bressoud's generalization of Rogers-Ramanujan combinatorial identities, by constructing bases of vacuum spaces for the principal Heisenberg subalgebra of standard $\widehat{\mathfrak{sl}}_{2}$-modules, parametrized with partitions satisfying certain difference 2 conditions. In this paper we define quasi-particles in the principal picture of $\widehat{\mathfrak{sl}}_{2}$ and construct quasi-particle monomial bases of standard $\widehat{\mathfrak{sl}}_{2}$-modules for which principally specialized characters are given as products of sum sides of the corresponding analytic Rogers-Ramanujan-type identities with the character of the Fock space for the principal Heisenberg subalgebra.

math.QA↗

arXiv2013

Principal subspaces for quantum affine algebra $U_q(A_n^{(1)})$

We consider principal subspace W(Λ) of integrable highest weight module L(Λ) for quantum affine algebra $U_q(\hat{\mathfrak{sl}}_{n+1})$. We introduce quantum analogues of the quasi-particles associated with the principal subspaces for $\hat{\mathfrak{sl}}_{n+1}$ and discover certain relations among them. By using these relations we find, for certain highest weight Λ, combinatorial bases of principal subspace W(Λ) in terms of monomials of quantum quasi-particles.

math.QA↗