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.
.dvi version (for previewing)
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