Parabolic Sheaves on Surfaces and Affine Lie Algebra Gl N

ar X iv : m at h / 99 03 18 1 v 1 [ m at h . A G ] 3 0 M ar 1 99 9 PARABOLIC SHEAVES ON SURFACES AND AFFINE LIE ALGEBRA

Ju l 2 00 6 Framed Rank r Torsion - free Sheaves on C P 2 and Representations of the Affine Lie

We construct geometric realizations of the r-colored bosonic and fermionic Fock space on the equivariant cohomology of the moduli space of framed rank r torsion-free sheaves on CP 2. Using these constructions, we realize geometrically all level one irreducible representations of the affine Lie algebra gl(r). The cyclic group Z k acts naturally on the moduli space of sheaves, and the fixed-point...

Modules of the toroidal Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

Realization of locally extended affine Lie algebras of type $A_1$

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

LEFT-SYMMETRIC ALGEBRAS FOR gl(n)

We study the classification problem for left-symmetric algebras with commutation Lie algebra gl(n) in characteristic 0. The problem is equivalent to the classification of étale affine representations of gl(n). Algebraic invariant theory is used to characterize those modules for the algebraic group SL(n) which belong to affine étale representations of gl(n). From the classification of these modu...