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Original Articles

MIXED TENSOR REPRESENTATIONS AND RATIONAL REPRESENTATIONS FOR THE GENERAL LINEAR LIE SUPERALGEBRAS

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Pages 839-857 | Published online: 01 Feb 2007

REFERENCES

  • Benkart , G.M. , Britten , D.J. and Lemire , F.W. 1990 . Stability in Modules for Classical Lie Algebras – A Constructive Approach . Memoirs of Amer Math. Soc. , 430
  • Benkart , G. , Chakrabarti , M. , Halverson , T. , Leduc , R. , Lee , C. and Stroomer , J. 1994 . Tensor Product Representations of General Linear Groups and their Connection with the Brauer Algebras . Journal of Algebra. , 166 : 529 – 567 .
  • Berele , A. and Regev , A. 1987 . Hook Young Diagrams with Applications to Combinatorics and Representations of Lie Superalgebras . Adv. in Math. , 64 : 118 – 175 .
  • Berele , A. and Regev , A. 1985 . Complex Parameters for the Representations of some Superalgebras . Communications in Algebra , 13 : 181 – 246 .
  • Halverson , T. 1996 . Characters of the Centralizer Algebras of Mixed Tensor Representations of and the Quantum Group . Pacific Journal of Mathematics , 174 : 359 – 410 .
  • Hanlon , P. 1985 . On the Decomposition of the Tensor Algebra of the Classical Lie Superalgebras . Adv. in Math. , 56 : 238 – 282 .
  • Kac , V. 1978 . Representations of Classical Lie Superalgebras . Differential Geometrical Methods in Mathematical Physics II, Lecture Notes in Mathe., Springer-Verlag, Berlin , 676 : 597 – 626 .
  • Kosuda , M. and Murakami , J. 1993 . Centralizer Algebras of the Mixed Tensor Representations of Quantum Algebra Osaka . J. of Math. , 30 : 475 – 507 .
  • Koike , K. 1989 . On the Decomposition of Tensor Products of the Representations of the Classical Groups: By Means of Universal Characters . Adv. in Math. , 74 : 57 – 86 .
  • Schur , I. 1901 . Uber eine Klasse von Matrizen, die sich einer gegeben Matrix zuordenen lassen . : 1 – 72 . reprinted in Gessamelte Abhandlungen
  • Schur , I. 1927 . Uber die rationalen Darstellungen der allgemeinen linearen Gruppe, Preuss . Akad. Wiss. Sitz , 3 : 68 – 85 . reprinted in Gessamelte Abhandlungen
  • Stembridge , J.R. 1987 . Rational Tableaux and the Tensor Algebra of . J. of Combinatorial Theory A , 46 : 79 – 120 .
  • Van der Jeugt , J. , Hughes , J.W.B. , King , R.C. and Thierry-Mieg , J. 1990 . A Character Formula for Singly-atypical Modules of the Lie Superalgebra . Communications in Algebra , 18 : 3453 – 3481 .

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