``Combinatorial Proofs of Capelli and Turnbull's identities from classical invariant theory'' (with Dominique Foata).

This is a historic paper: it is the first (R1) of v.1 of Electronic Journal of Combinatorics.

Capelli's identities was central in Hermann's Weyl's approach to the representation theory of the classical groups, in his classical `terrible and wonderful' (-R. Howe) book. Roger Howe revived the interest in Capelli's identity, and with Umeda found an anti-symmetric analog. In this paper, Dominique and I give a combinatorial proof. Foata's student, Yacob Akiba, used our combinatorial approach to give a combinatorial proof of the Howe-Umeda (also found independently by Kostant and Sahi) identity.

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Added Dec. 20, 2010: Darij Grinberg kinldy prepared an Errata Sheet

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