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Goran Trupčević

Publications and source records attributed to Goran Trupčević.

10 recordsLinked to original sources
arXiv2026

Generating sets of standard modules for $D_4^{(1)}$

Let $\widetilde{\mathfrak g}$ be an affine Lie algebra of type $D_4^{(1)}$ and $L(Λ)$ its standard module of level $k$ with highest weight vector $v_Λ$. We define Feigin--Stoyanovsky's type subspace as $W(Λ)=U(\widetilde{\mathfrak g}_{1})\,v_Λ$, where $\widetilde{\mathfrak g}=\widetilde{\mathfrak g}_{-1}\oplus\widetilde{\mathfrak g}_{0}\oplus\widetilde{\mathfrak g}_{1}$ is a $\mathbb{Z}$-gradation of $\widetilde{\mathfrak g}$ associated with a $\mathbb{Z}$-gradation $\mathfrak g=\mathfrak g_{-1}\oplus\mathfrak g_{0}\oplus\mathfrak g_{1}$. Using vertex operator relations, we reduce the Poincaré--Birkhoff--Witt spanning set of $W(Λ)$, and describe it in terms of difference and initial conditions. The spanning set of the whole standard module $L(Λ)$ can be obtained as a limit of the spanning set for $W(Λ)$.

math.QA↗
arXiv2025

Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$

In the previous paper, the authors proved linear independence of the combinatorial spanning set for standard $C_\ell^{(1)}$-module $L(kΛ_0)$ by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace $W(kΛ_0)$ of $C_{2\ell}^{(1)}$-module $L(kΛ_0)$. In this note we extend this argument for $C_{1}^{(1)}\cong A_{1}^{(1)}$ to all standard $A_{1}^{(1)}$-modules $L(Λ)$. In the proof we use a coefficient of an intertwining operator of the type $\binom{L(Λ_2)}{L(Λ_1)\ L(Λ_1)}$ for standard $C_{2}^{(1)}$-modules.

math.QA↗
arXiv2024

Linear independence for $C_\ell^{(1)}$ by using $C_{2\ell}^{(1)}$

In this note we prove linear independence of the combinatorial spanning set for standard $C_\ell^{(1)}$-module $L(kΛ_0)$ by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace $W(kΛ_0)$ of $C_{2\ell}^{(1)}$-module $L(kΛ_0)$. It should be noted that the proof of linear independence for the basis of $W(kΛ_0)$ is obtained by using simple currents and intertwining operators in the vertex operator algebra $L(kΛ_0)$.

math.QA↗
arXiv2017

Presentations of Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebras of type $C_\ell^{(1)}$

Feigin-Stoyanovsky's type subspace $W(Λ)$ of a standard $\tilde{\mathfrak g}$-module $L(Λ)$ is a $\tilde{\mathfrak g}_1$-submodule of $L(Λ)$ generated by the highest-weight vector $v_Λ$, where $\tilde{\mathfrak g}_1$ is a certain commutative subalgebra of $\tilde{\mathfrak g}$. Based on the description of basis of $W(Λ)$ for $\tilde{\mathfrak g}$ of type $C_\ell^{(1)}$, we give a presentation of this subspace in terms of generators and relations $$W(Λ)\simeq U(\tilde{\mathfrak g}_1^-)/J.$$

math.QA↗
arXiv2017

Bases of standard modules for affine Lie algebras of type $C_\ell^{(1)}$

Feigin-Stoyanovsky's type subspaces for affine Lie algebras of type $C_\ell^{(1)}$ have monomial bases with a nice combinatorial description. We describe bases of whole standard modules in terms of semi-infinite monomials obtained as "a limit of translations" of bases for Feigin-Stoyanovsky's type subspaces.

math.QA↗
arXiv2016

Bases of Feigin-Stoyanovsky's type subspaces for $C_\ell^{(1)}$

In this paper we construct combinatorial bases of Feigin-Stoyanovsky's type subspaces of standard modules for level $k$ affine Lie algebra $C_\ell^{(1)}$. We prove spanning by using annihilating field $x_θ(z)^{k+1}$ of standard modules. In the proof of linear independence we use simple currents and intertwinining operators whose existence is given by fusion rules.

math.QA↗
arXiv2008

Combinatorial bases of Feigin-Stoyanovsky's type subspaces of higher-level standard $\tilde{\gsl}(\ell+1,\C)$-modules

Let $\tilde{\mathfrak g}$ be an affine Lie algebra of the type $A_\ell^{(1)}$. We find a combinatorial basis of Feigin-Stoyanovsky's type subspace $W(Λ)$ given in terms of difference and initial conditions. Linear independence of the generating set is proved inductively by using coefficients of intertwining operators. A basis of $L(Λ)$ is obtained as an "inductive limit" of the basis of $W(Λ)$.

math.QA↗
arXiv2008

Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 1 standard modules for $\tilde{\mathfrak sl}(\ell+1,\C)$

Let $\tilde{\mathfrak g}$ be an affine Lie algebra of type $A_\ell^{(1)}$. Suppose we're given a $\mathbb Z$-gradation of the corresponding simple finite-dimensional Lie algebra ${\mathfrak g}={\mathfrak g}_{-1}\oplus{\mathfrak g}_0 \oplus {\mathfrak g}_1$; then we also have the induced $\mathbb Z$-gradation of the affine Lie algebra $$\tilde{\mathfrak g}=\tilde{\mathfrak g}_{-1} \oplus \tilde{\mathfrak g}_0 \oplus \tilde{\mathfrak g}_1.$$ Let $L(Λ)$ be a standard module of level 1. Feigin-Stoyanovsky's type subspace $W(Λ)$ is the $\tilde{\mathfrak g}_1$-submodule of $L(Λ)$ generated by the highest-weight vector $v_Λ$, $$W(Λ)=U(\tilde{\mathfrak g}_1)\cdot v_Λ\subset L(Λ).$$ We find a combinatorial basis of $W(Λ)$ given in terms of difference and initial conditions. Linear independence of the generating set is proved inductively by using coefficients of intertwining operators. A basis of $L(Λ)$ is obtained as an ``inductive limit'' of the basis of $W(Λ)$.

math.QA↗