Geodesic
Hilbert series, Howe duality and branching for classical groups
Thomas J. Enright1 ; Jeb F. Willenbring2
1Department of Mathematics, University of California at San Diego, La Jolla, CA 92093-0112, United States
2Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, United States
Annals of mathematics, Tome 159 (2004) no. 1, pp. 337-375
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An extension of the Littlewood Restriction Rule is given that covers all pertinent parameters and simplifies to the original under Littlewood’s hypotheses. Two formulas are derived for the Gelfand-Kirillov dimension of any unitary highest weight representation occurring in a dual pair setting, one in terms of the dual pair index and the other in terms of the highest weight. For a fixed dual pair setting, all the irreducible highest weight representations which occur have the same Gelfand-Kirillov dimension.

DOI : 10.4007/annals.2004.159.337

Thomas J. Enright  1   ; Jeb F. Willenbring  2

1 Department of Mathematics, University of California at San Diego, La Jolla, CA 92093-0112, United States
2 Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, United States 
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Thomas J. Enright; Jeb F. Willenbring. Hilbert series, Howe duality and branching for classical groups. Annals of mathematics, Tome 159 (2004) no. 1, pp. 337-375. doi: 10.4007/annals.2004.159.337

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