Quasi-particle fermionic formulas for \((k, 3)\)-admissible configurations

DOI10.2478/s11533-011-0127-7zbMath1288.17016arXiv1107.3900OpenAlexW2029141955MaRDI QIDQ424100

Mirko Primc, Miroslav Jerković

Publication date: 31 May 2012

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3900

zbMATH Keywords

affine Lie algebrasadmissible configurationsFeigin-Stoyanovsky type subspacesfermionic-type formulasquasi-particle bases

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Vertex operators; vertex operator algebras and related structures (17B69)

Related Items (12)

Vertex operators and principal subspaces of level one for \(U_q(\widehat{\mathfrak{sl}}_2)\) ⋮ Vertex-algebraic structure of principal subspaces of basic \(D_4^{(3)}\)-modules ⋮ Principal subspaces of higher-level standard $\widehat{\mathfrak{sl}(n)}$-modules ⋮ Higher level vertex operators for \(U_q \left( \widehat{\mathfrak {sl}}_2\right)\) ⋮ Combinatorial bases of principal subspaces for the affine Lie algebra of type \(B_2^{(1)}\) ⋮ Vertex-algebraic structure of principal subspaces of the basic modules for twisted affine Lie algebras of type \(A_{2n-1}^{(2)}\), \(D_n^{(2)}\), \(E_6^{(2)}\) ⋮ A note on principal subspaces of the affine Lie algebras in types Bl(1),Cl(1),F4(1) and G2(1) ⋮ Quasi-particle Bases of Principal Subspaces of Affine Lie Algebras ⋮ Presentations of the principal subspaces of the higher-level standard \(\widehat{\mathfrak{sl}(3)}\)-modules ⋮ Principal subspaces for the quantum affine vertex algebra in type \(A_1^{( 1 )}\) ⋮ Principal subspaces of twisted modules for certain lattice vertex operator algebras ⋮ Principal subspaces for the affine Lie algebras in types \(D, E\) and \(F\)

Cites Work

• Character formulas for Feigin-Stoyanovsky's type subspaces of standard \(\mathfrak{sl}(3, \mathbb{C})^{\sim}\)-modules
• The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators
• Principal subspaces of higher-level standard \(\widehat{\mathfrak{sl}(3)}\)-modules
• Vertex-algebraic structure of the principal subspaces of certain \(A_1^{(1)}\)-modules. II: Higher-level case
• Fermionic characters and arbitrary highest-weight integrable \({\widehat{\mathfrak{sl}}}_{r+1}\)-modules
• Recurrence relations for characters of affine Lie algebra \(A_{\ell}^{(1)}\)
• The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
• Basic representations of affine Lie algebras and dual resonance models
• Unitary representations of some infinite dimensional groups
• Generalized vertex algebras and relative vertex operators
• Vertex operator construction of standard modules for \(A_ n^{(1)}\)
• Bosonic formulas for (\(k, l\))-admissible partitions
• Fermionic formulas for \((k,3)\)-admissible configurations
• Particle content of the \((k,3)\)-configurations
• Functional models of the representations of current algebras and semi-infinite Schubert cells
• Combinatorial constructions of modules for infinite-dimensional Lie algebras. I: Principal subspace
• Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types \(A,D,E\)
• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of higher-level standard \(\tilde {\mathfrak {sl}} (\ell +1, \mathbb C)\)-modules
• Combinatorial Bases of Feigin–Stoyanovsky's Type Subspaces of Level 2 Standard Modules for
• Combinatorial Bases of Feigin–Stoyanovsky's Type Subspaces of Level 1 Standard Modules for
• INTERTWINING VERTEX OPERATORS AND CERTAIN REPRESENTATIONS OF $\widehat{\mathfrak{sl}(n)}$
• THE ROGERS–RAMANUJAN RECURSION AND INTERTWINING OPERATORS
• VERTEX-ALGEBRAIC STRUCTURE OF THE PRINCIPAL SUBSPACES OF CERTAIN $A_{1}^{(1)}$-MODULES, I: LEVEL ONE CASE
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