Robinson-Schensted correspondence for party algebras

A. Vidhyaa and A. Tamilselvib,*

Robinson-Schensted correspondence for party algebras

Authors :

A. Vidhya^a and A. Tamilselvi^b,*

Author Address :

^aRamanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai-600 005, Tamil Nadu, India.
^bAnna University, MIT Campus, Chennai - 600 044, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, we construct a bijective proof of the identity $n^k=sum_{ ilde{[lambda]}in Lambda_n^k}f^{ ilde{[lambda]}}m_k^{ ilde{[lambda]}}$, where $m_k^{ ilde{[lambda]}}$ is the multiplicity of the irreducible representation of $mathds{Z}_rwr S_n$ module indexed by $ ilde{[lambda]}in Lambda_n^k$, $f^{ ilde{[lambda]}}$ is the degree of the corresponding representation indexed by $ ilde{[lambda]}in Lambda_n^k$ and $Lambda_n ^k ={ ilde{[lambda]}vdash n| sum_{i=1}^k i|lambda^{(i)}|=k}$. We give the proof of Robinson-Schensted correspondence for the party algebras which gives the bijective proof of party diagrams and the pairs of vacillating tableaux.