Functional equations for character series associated with matrices
Author:
Edward Formanek
Journal:
Trans. Amer. Math. Soc. 294 (1986), 647663
MSC:
Primary 15A72; Secondary 16A38
MathSciNet review:
825728
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Abstract: Let be either the ring of invariants or the trace ring of generic matrices. Then has a character series which is a symmetric rational function of commuting variables . The main result is that if , then satisfies the functional equation , where is the Krull dimension of .
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Edward
Formanek, Invariants and the ring of generic matrices, J.
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 [1]
 E. Formanek, Invariants and the ring of generic matrices, J. Algebra 89 (1984), 178223. MR 748233 (85g:15031)
 [2]
 M. Hochster and J. L. Roberts, Rings of invariants of reductive groups acting on regular rings are CohenMacaulay, Adv. in Math. 13 (1974), 115175. MR 0347810 (50:311)
 [3]
 G. James and A. Kerber, The representation theory of the symmetric group, AddisonWesley, Reading, Mass. 1981. MR 644144 (83k:20003)
 [4]
 L. Le Bruyn, The functional equation for Poincaré series of trace rings of generic matrices, Israel J. Math. (to appear). MR 829364 (87e:16041)
 [5]
 I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Univ. Press (Clarendon), Oxford, 1979. MR 553598 (84g:05003)
 [6]
 M. P. Murthy, A note on factorial rings, Arch. Math. 15 (1964), 418420. MR 0173695 (30:3905)
 [7]
 C. Procesi, The invariant theory of matrices, Adv. in Math. 19 (1976), 306381. MR 0419491 (54:7512)
 [8]
 L. H. Rowen, Polynomial identities in ring theory, Academic Press, New York, 1980. MR 576061 (82a:16021)
 [9]
 T. A. Springer, Invariant theory, Lecture Notes in Math., vol. 585, SpringerVerlag, Berlin and New York, 1977. MR 0447428 (56:5740)
 [10]
 R. P. Stanley, Hilbert functions of graded algebras, Adv. in Math. 28 (1978), 5783. MR 0485835 (58:5637)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198608257288
PII:
S 00029947(1986)08257288
Article copyright:
© Copyright 1986
American Mathematical Society
