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Decomposition of exterior algebras. (English) Zbl 0851.57040

Gross, Kenneth I. (ed.) et al., Representation theory and harmonic analysis. A conference in honor of Ray A. Kunze, January 12-14, 1994, Cincinnati, OH, USA. Providence, RI: American Mathematical Society. Contemp. Math. 191, 99-105 (1995).
Summary: Consider the group \(\text{GL}(p,\mathbb{C}) \times \text{GL}(q,\mathbb{C})\) acting on \(\mathbb{C}^p \otimes \mathbb{C}^q\). We ask: How does \(\Lambda^* (\mathbb{C}^p \otimes \mathbb{C}^q)\) decompose under the induced action of \(\text{GL}(p,\mathbb{C}) \times \text{GL}(q,\mathbb{C})\)? In this paper, we determine the structure of the \(\text{GL} (p,\mathbb{C}) \times \text{GL}(q,\mathbb{C})\)-module \(\Lambda^* (\mathbb{C}^p \otimes \mathbb{C}^q)\).
For the entire collection see [Zbl 0827.00039].

MSC:

57T15 Homology and cohomology of homogeneous spaces of Lie groups
14F40 de Rham cohomology and algebraic geometry
57T10 Homology and cohomology of Lie groups
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