DOI QR코드

DOI QR Code

AN INVOLUTION ON THE SHIFTED RIM HOOK TABLEAUX

  • Lee, Jae-JIn (Department of Mathematics Hallym University)
  • Published : 2002.07.01

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

shifted rim hook tableaux;sign reversing involution

References

  1. 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
  2. Proc. Hallym Univ. jour. v.9 Rim Hooks on the Shifted Diagrams Jaejin Lee
  3. 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
  4. 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
  5. Commun. Korean Math. Soc. v.13 Combinatorial Proof for the Generalized Schur Identity
  6. 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
  7. Ph. D. thesis A theory of Shifted Young Tableaux D. R. Worley