# Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A,D,E

@article{Calinescu2009VertexalgebraicSO, title={Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A,D,E}, author={Corina Calinescu and James Lepowsky and Antun Milas}, journal={arXiv: Quantum Algebra}, year={2009} }

## 60 Citations

### Vertex-algebraic structure of principal subspaces of standard A_2^{(2)}-modules, I

- Mathematics
- 2014

Extending earlier work of the authors, this is the first in a series of papers devoted to the vertex-algebraic structure of principal subspaces of standard modules for twisted affine Kac-Moody…

### Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case

- Mathematics
- 2007

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine…

### Principal subspaces of twisted modules for certain lattice vertex operator algebras

- MathematicsInternational Journal of Mathematics
- 2019

This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices…

### Principal subspaces of basic modules for twisted affine Lie algebras, $q$-series multisums, and Nandi's identities

- Mathematics
- 2022

. We provide an observation relating several known and conjectured q -series identities to the theory of principal subspaces of basic modules for twisted aﬃne Lie algebras. We also state and prove…

### Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, II: higher level case

- Mathematics
- 2007

### Combinatorial bases of modules for affine Lie algebra B2(1)

- Mathematics
- 2010

We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B2(1) consisting of semi-infinite monomials. The main technical ingredient is a…

### Finite Dynkin diagrams The affine Kac –

- Mathematics
- 2019

We consider the principal subspaces of certain level k > 1 integrable highest weight modules and generalized Verma modules for the untwisted affine Lie algebras in types D, E and F . Generalizing the…

## References

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### Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case

- Mathematics
- 2007

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine…

### Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, II: higher level case

- Mathematics
- 2007

### (k,r)-admissible configurations and intertwining operators

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Certain combinatorial bases of Feigin-Stoyanovsky's type subspaces of level k standard modules for affine Lie algebra sl(r,C)\sptilde are parametrized by (k,r)-admissible configurations. In this note…

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We give an explicit construction of the affine Lie algebraA1(1) as an algebra of differential operators on ℂ[x1,x3,x5, ...]. This algebra is spanned by the creation and annihilation operators and by…

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We study the principal subspaces, introduced by B. Feigin and A. Stoyanovsky, of the level 1 standard modules for $\hat{\goth{sl}(l+1)}$ with $l \geq 2$. In this paper we construct exact sequences…

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We give a new interpretation and proof of the "quasi-particle" type character formulas for integrable representations of the simply-laced affine Kac-Moody algebras through a new "semi-infinite"…

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We study a class of representations of the Lie algebra of Laurent polynomials with values in the nilpotent subalgebra of sl(3). We derive Weyl-type (bosonic) character formulas for these…