Combinatorial bases of principal subspaces for the affine Lie algebra of type

Vertex-algebraic structure of principal subspaces of the basic modules for twisted affine Lie algebras of type A2n−1(2),Penn1, Sadowski2 2018Journal of Algebra122320View full textAdd to dashboardCite

“…These principal subspaces were also student in [AKS], [FFJMM], and in other works by these authors. Georgiev used the theory of vertex operator algebras and intertwining operators to construct combinatorial bases for principal subspaces of certain higher level standard modules for untwisted affine Lie algebras of type A, D, E in [G], and this work has since been extended to untwisted affine Lie algebras of type B, C by Butorac in [Bu1]- [Bu2] and to the quantum group case by Kožić in [Ko]. Principal subspaces of standard modules for more general lattice vertex operator algebras have been studied in [MPe], [P], and [Ka1]- [Ka2].…”

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

“…[16]), from which were easily obtained the Rogers-Ramanujan type character formulas. In [4] and [5] we extended Georgiev's construction of quasiparticle bases for principal subspaces of standard module L(kΛ 0 ) and generalized Verma module N (kΛ 0 ) of highest weight kΛ 0 , k ∈ N for affine Lie algebras of type B…”

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

“…Furthermore, integrability relations played an important role in the construction of monomial bases for certain substructures of g-modules such as principal subspaces (cf. [FS], [G], [Bu1], [Ka]) and Feigin-Stoyanovsky's type subspaces (cf. [P1], [P2], [JP], [T]).…”