An algorithmic Littlewood-Richardson rule
Ricky Ini Liu
DOI: 10.1007/s10801-009-0184-1
Abstract
We introduce a Littlewood-Richardson rule based on an algorithmic deformation of skew Young diagrams and present a bijection with the classical rule. The result is a direct combinatorial interpretation and proof of the geometric rule presented by Coskun ( 2000). We also present a corollary regarding the Specht modules of the intermediate diagrams.
Pages: 253–266
Keywords: keywords Littlewood-Richardson rule; Specht modules; Grassmannian
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References
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2. James, G.D.: A characteristic-free approach to the representation theory of Sn. J. Algebra 46(2), 430- 450 (1977)
3. Knutson, A., Tao, T.: Puzzles and (equivariant) cohomology of Grassmannians. Duke Math. J. 119(2), 221-260 (2003)
4. Peel, M.H., James, G.D.: Specht series for skew representations of symmetric groups. J. Algebra 56(2), 343-364 (1979)
5. Reiner, V., Shimozono, M.: Percentage-avoiding, northwest shapes and peelable tableaux. J. Combin. Theory Ser. A 82(1), 1-73 (1998)
6. Sagan, B.E.: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edn. Graduate Texts in Mathematics, vol.
203. Springer, New York (2001)
7. Stanley, R.P.: Enumerative Combinatorics, vol.
2. Cambridge Studies in Advanced Mathematics, vol.
62. Cambridge University Press, Cambridge (1999). With a foreword by Gian-Carlo Rota and