대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제17권3호
  • /
  • Pages.551-563
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  • 2002
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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AN INVOLUTION ON THE SHIFTED RIM HOOK TABLEAUX

  • Published : 2002.07.01
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Abstract

We Construct a Sign reversing involution on the Shifted rim hook tableaux with some conditions. Using the Stembridge's combinatorial interpretation for Morris' rule, this involution give a combinatorial proof of the orthogonality of the first kind for the spin characters of $S_{n}$.

Keywords

References

  1. Proc. Hallym Univ. jour. v.9 Rim Hooks on the Shifted Diagrams Jaejin Lee
  2. Commun. Korean Math. Soc. v.13 Combinatorial Proof for the Generalized Schur Identity
  3. Proc. London Math Soc. v.12 The spin representation of the symmetric group A. O. Morris https://doi.org/10.1112/plms/s3-12.1.55
  4. J. Combin. Theory (A) v.45 Shifted tableaux, Schur Q-functions and a conjecture of R. Stanley B. E. Sagan https://doi.org/10.1016/0097-3165(87)90047-1
  5. Advances in Math. v.74 Shifted tableaux and projective representations of symmetric groups J. R. Stembridge https://doi.org/10.1016/0001-8708(89)90005-4
  6. Advances in Math. v.50 A bijection proving orthogonality of the characters of Sn D. E. White https://doi.org/10.1016/0001-8708(83)90038-5
  7. Ph. D. thesis A theory of Shifted Young Tableaux D. R. Worley