The exterior algebra and ‘ Spin ’ of an orthogonal g - module Dmitri
نویسنده
چکیده
The symmetric algebra of a (finite-dimensional) g-module V is the algebra of polynomial functions on the dual space V . Therefore one can study the algebra of symmetric invariants using geometry of G-orbits in V ∗ . In case of the exterior algebra, ∧•V, lack of such geometric picture results by now in absence of general structure theorems for the algebra of skew-invariants (∧•V)g . One may find in the literature several interesting results related to skew-symmetric invariants. We only mention Kostant’s computation for cohomology of the nilradical of a parabolic subalgebra in g [Ko61] and R.Howe’s classification of “skew-multiplicity-free” g-modules [Ho95, ch. IV]. But the general situation still remains unsatisfactory, and developing of Invariant Theory in the skew-symmetric setting represents an attractive problem.
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