Journal of Lie Theory 16 (2006), No. 2, 393--405
Copyright Heldermann Verlag 2006
Alpha-Determinant Cyclic Modules of gln(C)
Sho Matsumoto
Graduate School of Mathematics, Kyushu University, Hakozaki Higashi-ku, Fukuoka 812-8581, Japan
shom@math.kyushu-u.ac.jp
Masato Wakayama
Faculty of Mathematics, Kyushu University, Hakozaki Higashi-ku, Fukuoka 812-8581, JAPAN
wakayama@math.kyushu-u.ac.jp
[Abstract-pdf]
The alpha-determinant unifies and interpolates the notion of the determinant and permanent. We determine the irreducible decomposition of the cyclic module of $\frak{gl}_n({\Bbb C})$ defined by the alpha-determinant. The degeneracy of the irreducible decomposition is determined by the content polynomial of a given partition.
Keywords: Schur module, Young symmetrizer, permanent, Frobenius notation, irreducible decomposition, cyclic module.
MSC: 06B15, 15A15
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