Combinatorial Bases of Feigin–Stoyanovsky's Type Subspaces of Level 2 Standard Modules for

Combinatorial bases of modules for affine Lie algebra B 2(1)

“…Let g be a complex simple Lie algebra of type B 2 and let h be a Cartan subalgebra of g. Let g = h + g α be a root space decomposition of g. The corresponding root system R may be realized in R 2 with the canonical basis ε 1 ε 2 as…”

“…Since the list of all possible Z-gradings (1) coincides with the list of all possible level 1 simple currents constructed in [8], the results and methods used in [2,30] and this paper give hope that the construction in [27] might be extended to all standard modules of all classical affine Lie algebras by using intertwining operators. In return, one should expect a rich and interesting combinatorial structure behind this construction, on one side extending combinatorics of infinite paths used in [20], and on the other side extending ( + 1)-admissible configurations -combinatorial objects introduced and studied in a series of papers [9,10].…”

“…A new understanding came from the works of G. Georgiev [17] and S. Capparelli, J. Lepowsky and A. Milas [5,6] based on a general idea of J. Lepowsky to use intertwining vertex operators to build bases of standard modules and obtain Rogers-Ramanujan type recursions for their graded dimensions. Their way of using intertwining operators inspired a simpler proof of linear independence for A (1) in [28], and new constructions for D (1) 4 by I. Baranović in [2] and for A (1) by G. Trupčević in [30] for all possible Z-gradings (1).…”

Characters of Feigin-Stoyanovsky's type subspaces of level one modules for affine Lie algebras of types Al(1) and D4(1)

“…Principal subspaces were introduced by B. L. Feigin and A. Stoyanovsky in [13] where they gave a construction of bases of standard modules L(Λ) consisting of semi-infinite monomials and monomial bases of their principal subspaces, and also calculated characters of both principal subspaces and the whole standard modules for affine Lie algebrag of type A (1) 1 . A similar approach was used by M. Primc in [19,20] where he constructed semi-infinite monomial bases for all standard modules for affine Lie algebras of type A (1) ℓ and for basic modules L(Λ 0 ) for any classical affine Lie algebra.…”

Presentations of Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebras of type Cl(1)

“…Another type of principal subspaces, called Feigin-Stoyanovsky's type subspaces, was introduced by M. Primc who constructed bases of these subspaces in different cases ( [24][25][26]18]). These kind of subspaces were further studied by many authors ( [28,15,10,11,1,13,14,2,4,5,17,30], etc.) and the knowledge of presentation presents an important question in this study ([6-9, 27, 23]).…”