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math.RA2008
Laplacian spectrum for the nilpotent Kac-Moody Lie algebras
Dmitry Fuchs, Constance Wilmarth
We prove that the maximal nilpotent subalgebra of a Kac-Moody Lie algebra has an (essentially unique) Euclidean metric with respect to which the Laplace operator in the chain compl…
math.RT2008
Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras
Dmitry Fuchs, Constance Wilmarth
We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac-Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Li…