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Marijana Butorac

Publications and source records attributed to Marijana Butorac.

15 recordsLinked to original sources
arXiv2026

Quasi-particles and the Kanade-Russell and Kurşungöz formula for Capparelli's identity

We construct a quasi-particle basis of the integrable highest weight module of highest weight $3Λ_0$ for the twisted affine Lie algebra of type $A_2^{(2)}$ in the principal realization. More specifically, by introducing the concept of polychromatic quasi-particle and finding relations among quasi-particles, we construct the spanning set of the standard module. Finally, its linear independence is proved by using Kanade-Russell and Kurşungöz's Andrews-Gordon type series of Capparelli's identities.

math.QA↗
arXiv2025

On two families of quantum vertex algebras of FRT-type

We consider two new families of quantum vertex algebras which are associated with the type $A$ trigonometric $R$-matrix and elliptic $R$-matrix of the eight-vertex model. We show that their $ϕ$-coordinated representation theory is governed by the so-called FRT-operator, $h$-adically restricted operator satisfying the FRT-relation, and we demonstrate some applications of this result. Finally, in the elliptic case, we investigate the properties of the quantum determinant associated with the corresponding quantum vertex algebra.

math.QA↗
arXiv2024

Lepowsky's and Wakimoto's product formulas for the affine Lie algebras $C_l^{(1)}$

In this paper, we recall Lepowsky's and Wakimoto's product character formulas formulated in a new way by using arrays of specialized weighted crystals of negative roots for affine Lie algebras of type $C_l^{(1)}$, $D_{l+1}^{(2)}$ and $A_{2l}^{(2)}$. Lepowsky-Wakimoto's infinite periodic products appear as one side of (conjectured) Rogers-Ramanujan-type combinatorial identities for affine Lie algebras of type $C_l^{(1)}$.

math.RT↗
arXiv2023

Semi-infinite construction for the double Yangian of type $A_1^{(1)}$

We consider certain infinite dimensional modules of level 1 for the double Yangian $\text{DY}(\mathfrak{gl}_2)$ which are based on the Iohara-Kohno realization. We show that they possess topological bases of Feigin-Stoyanovsky-type, i.e. the bases expressed in terms of semi-infinite monomials of certain integrable operators which stabilize and satisfy the difference two condition. Finally, we give some applications of these bases to the representation theory of the corresponding quantum affine vertex algebra.

math.QA↗
arXiv2022

Combinatorial bases of standard modules of twisted affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$: rectangular highest weights

We consider the standard modules of rectangular highest weights of affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$. By using vertex algebraic techniques we construct the combinatorial bases for standard modules and their principal subspaces and parafermionic spaces. Finally, we compute the corresponding character formulae and, as an application, we obtain two new families of combinatorial identities.

math.RT↗
arXiv2021

On the Heisenberg algebra associated with the rational $R$-matrix

We associate a deformation of Heisenberg algebra to the suitably normalized Yang $R$-matrix and we investigate its properties. Moreover, we construct new examples of quantum vertex algebras which possess the same representation theory as the aforementioned deformed Heisenberg algebra.

math.QA↗
arXiv2020

Principal subspaces for the quantum affine vertex algebra in type $A_1^{(1)}$

By using the ideas of Feigin and Stoyanovsky and Calinescu, Lepowsky and Milas we introduce and study the principal subspaces associated with the Etingof-Kazhdan quantum affine vertex algebra of integer level $k\geqslant 1$ and type $A_1^{(1)}$. We show that the principal subspaces possess the quantum vertex algebra structure, which turns to the usual vertex algebra structure of the principal subspaces of generalized Verma and standard modules at the classical limit. Moreover, we find their topological quasi-particle bases which correspond to the sum sides of certain Rogers-Ramanujan-type identities.

math.QA↗
arXiv2020

Parafermionic bases of standard modules for affine Lie algebras

In this paper we construct combinatorial bases of parafermionic spaces associated with the standard modules of the rectangular highest weights for the untwisted affine Lie algebras. Our construction is a modification of G. Georgiev's construction for the affine Lie algebra $\widehat{\mathfrak sl}(n+1,\mathbb C)$---the constructed parafermionic bases are projections of the quasi-particle bases of the principal subspaces, obtained previously in a series of papers by the first two authors. As a consequence we prove the character formula of A. Kuniba, T. Nakanishi and J. Suzuki for all non-simply-laced untwisted affine Lie algebras.

math.QA↗
arXiv2019

$h$-adic quantum vertex algebras associated with rational $R$-matrix in types $B$, $C$ and $D$

We introduce the $h$-adic quantum vertex algebras associated with the rational $R$-matrix in types $B$, $C$ and $D$, thus generalizing the Etingof--Kazhdan's construction in type $A$. Next, we construct the algebraically independent generators of the center of the $h$-adic quantum vertex algebra in type $B$ at the critical level, as well as the families of central elements in types $C$ and $D$. Finally, as an application, we obtain commutative subalgebras of the dual Yangian and the families of central elements of the appropriately completed double Yangian at the critical level, in types $B$, $C$ and $D$.

math.QA↗
arXiv2019

Principal subspaces for the affine Lie algebras in types $D$, $E$ and $F$

We consider the principal subspaces of certain level $k\geqslant 1$ integrable highest weight modules and generalized Verma modules for the untwisted affine Lie algebras in types $D$, $E$ and $F$. Generalizing the approach of G. Georgiev we construct their quasi-particle bases. We use the bases to derive presentations of the principal subspaces, calculate their character formulae and find some new combinatorial identities.

math.QA↗
arXiv2015

Quasi-particle bases of principal subspaces for the affine Lie algebras of types $B_{l}^{(1)}$ and $C_{l}^{(1)}$

Generalizing our earlier work, we construct quasi-particle bases of principal subspaces of standard module $L_{X_l^{(1)}}(kΛ_0)$ and generalized Verma module $N_{X_l^{(1)}}(kΛ_0)$ at level $k\geq 1$ in the case of affine Lie algebras of types $B_l^{(1)}$ and $C_l^{(1)}$. As a consequence, from quasi-particle bases, we obtain the graded dimensions of these subspaces.

math.QA↗
arXiv2012

Combinatorial bases of principal subspaces for affine Lie algebra of type B_2^(1)

We consider principal subspaces $W_{L(kΛ_0)}$ and $W_{N(kΛ_0)}$ of standard module $L(kΛ_0)$ and generalized Verma module $N(kΛ_0)$ at level $k\geq 1$ for affine Lie algebra of type $B_2^{(1)}$. By using the theory of vertex operator algebras, we find combinatorial bases of principal ubspaces in terms of quasi-particles. From quasi-particle bases, we obtain character formulas for $W_{L(kΛ_0)}$ and $W_{N(kΛ_0)}$.

math.QA↗