Combinatorial bases of modules for affine Lie algebra B_2^(1)

Mirko Primc

Combinatorial bases of modules for affine Lie algebra B_2^(1)

Quantum Algebra 2012-03-30 v2

Authors: Mirko Primc

Abstract

In this paper we construct bases of standard (i.e. integrable highest weight) modules $L(\Lambda)$ for affine Lie algebra of type $B_2\sp{(1)}$ consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces $W(\Lambda)$ of $L(\Lambda)$ by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence $W(k\Lambda_0)$ for $B_2\sp{(1)}$ and the integrable highest weight module $L(k\Lambda_0)$ for $A_1\sp{(1)}$ have the same parametrization of combinatorial bases and the same presentation $\mathcal P/\mathcal I$ \,.

Keywords

highest weight modules lie algebras and modules irreducible modules for lie algebras

Cite

@article{arxiv.1002.3535,
  title  = {Combinatorial bases of modules for affine Lie algebra B_2^(1)},
  author = {Mirko Primc},
  journal= {arXiv preprint arXiv:1002.3535},
  year   = {2012}
}

Comments

AMS-LaTeX, 29 pages, to appear in Central European Journal of Mathematics. v2: The claim that presentation for B_2^(1) implies linear independence for A_1^(1) is incorrect and omitted; other minor changes; a new section on vertex operator formula is added

Combinatorial bases of modules for affine Lie algebra B_2^(1)

Abstract

Keywords

Cite

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