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Kožić, Slaven

doi:10.1016/j.jalgebra.2016.01.041

Cited by 5 publications

(7 citation statements)

References 42 publications

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“…This connection was further studied by many authors, in particular in [3], [6,7], [8][9][10][11], [12], [13,14], [18], [24], [28,29], [30,31] and others. More recently, Slaven Kožić in [22,23] showed that character formulas for level 1 principal subspaces associated with the integrable highest weight module of quantum affine algebra U q ( sl 2 ) coincide with the character formulas found in [16].…”

Section: Introductionmentioning

confidence: 53%

Quasi-particle bases of principal subspaces of the affine Lie algebra of type G_2^{(1)}

Butorac

2017

Glas. Mat. Ser. III

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The aim of this work is to construct the quasi-particle basis of principal subspace of standard module of highest weight kΛ 0 of level k ≥ 1 of affine Lie algebra of type G (1) 2 by means of which we obtain the basis of principal subspace of generalized Verma module. 2010 Mathematics Subject Classification. 17B67, 17B69, 05A19. Key words and phrases. Affine Lie algebras, vertex operator algebras, principal subspaces, quasi-particle bases. This work has been supported in part by the Croatian Science Foundation under the project 2634., by the Croatian Scientific Centre of Excellence QuantiXLie and by University of Rijeka research grant 13.14.1.2.02.

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Section: Introductionmentioning

confidence: 53%

Quasi-particle bases of principal subspaces of the affine Lie algebra of type G_2^{(1)}

Butorac

2017

Glas. Mat. Ser. III

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“…By employing the second part of Theorem 2.14 and Koyama's realization of intertwining operators for U q ( sl 2 ) (see [Koy]), we prove the main result of this section: For c = 1 the similar basis was already found in [Ko3]. However, this was a basis for W 1,q , a certain subspace of a much bigger (nongraded) nonlocal q-vertex algebra generated by x(z) = x + 1 (z) ∈ E(L(Λ 0 )) (which satisfied a slightly modified version of (0.3)).…”

Section: Introductionmentioning

confidence: 53%

“…In this paper, we continue our research on vertex algebraic structures arising from FrenkelJing operators x ± 1 (z) for U q ( sl 2 ), which was initiated in [Ko3]. So far there were several fruitful approaches to associating vertex algebra-like theories with the various quantum objects, such as quantum affine algebras or Yangians, which resulted in some fundamental results and important constructions (cf.…”

Section: Introductionmentioning

confidence: 94%

“…The case c = 1, n = 0 was solved in [Ko3] using the slightly different vertex algebraic setting. The results therein imply that the set B 1,0 = x 1,0 (z, t) r 1 x 1,0 (z, t) r 2 .…”

Section: Theorem 214 Let S Be a Quasi-commutative Subset Of E(l) T mentioning

confidence: 99%

“…In Section 1, we establish the notation and recall some well-known results from the theory of quantum affine algebras. Although the exposition is to a great extent similar to the preliminary section in [Ko3], we decided to include it in order to make this paper as self-contained as possible.…”

Section: Introductionmentioning

confidence: 99%

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Higher level vertex operators for $$U_q \left( \widehat{\mathfrak {sl}}_2\right) $$ U q sl ^ 2

Kožić

2017

Sel. Math. New Ser.

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Abstract. We study graded nonlocal 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 q-vertex algebras V c,1 , c ≥ 1, associated with the principal subspaces W (cΛ 0 ) of the integrable highest weight U q ( sl 2 )-modules L(cΛ 0 ). Using quantum integrability, we derive combinatorial bases for V c,1 and compute the corresponding character formulae. IntroductionIn their work [LP], J. Lepowsky and M. Primc found the, so-called integrability condition for the affine Kac-Moody Lie algebra sl 2 ,on a level c integrable sl 2 -module. In general, (0.1) holds on an arbitrary level c integrable g-module, when the simple root α is replaced by the maximal root of the untwisted affine Kac-Moody Lie algebra g. In this paper, we continue our research on vertex algebraic structures arising from FrenkelJing operators x ± 1 (z) for U q ( sl 2 ), which was initiated in [Ko3]. So far there were several fruitful approaches to associating vertex algebra-like theories with the various quantum objects, such as quantum affine algebras or Yangians, which resulted in some fundamental results and important constructions (cf. [AB],[B],[EK],[FR],[L1]-[L4]). However, motivated by the role of integrability (0.1) in the representation theory of the affine Kac-Moody Lie algebras, we introduce graded nonlocal q-vertex algebras, certain new structures which are designed to make use of quantum integrability (0.2).2000 Mathematics Subject Classification. 17B37 (Primary), 17B69 (Secondary).

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Quasi-particle Bases of Principal Subspaces of Affine Lie Algebras

Butorac

2019

Springer INdAM Series

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Generalizing our earlier work, we construct quasi-particle bases of principal subspaces of standard module L X (1) l (kΛ 0 ) and generalized Verma module N X (1) l (kΛ 0 ) at level k ≥ 1 in the case of affine Lie algebras of types B(1) l and C (1) l . As a consequence, from quasi-particle bases, we obtain the graded dimensions of these subspaces. IntorductionLet g be a simple complex Lie algebra of type X l , with a Cartan subalgebra h, the set of simple roots Π = {α 1 , . . . , α l } and the triangular decomposition g = n − ⊕ h ⊕ n + , where n + is a direct sum of its one dimensional subalgebras corresponding to the positive roots. Denote by L(n + ) a subalgebra of untwisted affine Lie algebra g of type X(1) lLet V be a highest g-module with highest weight Λ and highest weight vector v Λ . We define the principal subspace W V of V asIn this paper we study principal subspaces of the generalized Verma module N X (1) l (kΛ 0 ) and its irreducible quotient L X (1) l (kΛ 0 ) at level k ≥ 1, defined over the affine Lie algebras of type B(1) l and C(1) l . The study of principal subspaces of standard (i.e., integrable highest weight) modules of the simply laced affine Lie algebras and its connection to Rogers-Ramanujan identities was initiated in the work of B. L. Feigin and A. V. Stoyanovsky [FS] and has been further developed in [AKS]

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Vertex operators and principal subspaces of level one for Uq(slˆ2

Cited by 5 publications

References 42 publications

Quasi-particle bases of principal subspaces of the affine Lie algebra of type G_2^{(1)}

Quasi-particle bases of principal subspaces of the affine Lie algebra of type G_2^{(1)}

Higher level vertex operators for $$U_q \left( \widehat{\mathfrak {sl}}_2\right) $$ U q sl ^ 2

Quasi-particle Bases of Principal Subspaces of Affine Lie Algebras

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