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A Direct Way to Find the Right Key of a Semistandard Young Tableau

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Abstract

The right key of a semistandard Young tableau is a tool used to find Demazure characters for \({sl_n(\mathbb{C})}\) . This paper gives methods to obtain the right and left keys by inspection of the semistandard Young tableau.

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References

  1. Aval, J.-C.: Keys and alternating sign matrices. Sém. Lothar. Combin. 59, Art. B59f (2008)

  2. Fulton W.: Young Tableaux. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  3. Lakshmibai V., Brown J.: Flag Varieties: an Interplay of Geometry, Combinatorics, and Representation Theory. Hindustan Book Agency, New Delhi (2009)

    MATH  Google Scholar 

  4. Lakshmibai, V., Seshadri, C.S.: Standard monomial theory. In: Ramanan, S., Musili, C., Kumar, N.M. (eds.) Proceedings of the Hyderabad Conference on Algebraic Groups, pp. 279–322. Manoj Prakashan, Madras (1991)

  5. Lascoux, A., Schützenberger, M.-P.: Keys and standard bases. In: Stanton, D. (ed.) Invariant Theory and Tableaux, pp. 125–144. Springer, New York (1990)

  6. Lenart C.: A unified approach to combinatorial formulas for Schubert polynomials. J. Algebraic Combin. 20(3), 263–299 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lenart C.: On the combinatorics of crystal graphs, I. Lusztig’s involution. Adv. Math. 211(1), 204–243 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lenart, C., Postnikov, A.: Affine Weyl groups in K-theory and representation theory. Int. Math. Res. Not. IMRN 2007, Art. rnm038 (2007)

  9. Mason S.: An explicit construction of type A Demazure atoms. J. Algebraic Combin. 29(3), 295–313 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Postnikov A., Stanley R.: Chains in the Bruhat order. J. Algebraic Combin. 29(2), 133–174 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Proctor, R., Willis, M.: Tableaux for key polynomials, Demazure characters, and atoms. Preprint

  12. Proctor, R., Willis, M.: Convexity of sets of Demazure tableaux, and relationship to flagged Schur functions. In preparation

  13. Reiner V., Shimozono M.: Key polynomials and a flagged Littlewood-Richardson rule. J. Combin. Theory Ser. A 70(1), 107–143 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  14. Reiner V., Shimozono M.: Straightening for standard monomials on Schubert varieties. J. Algebra 195(1), 130–140 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Willis, M.: New Descriptions of Demazure Tableaux and Right Keys, with Applications to Convexity. Ph.D. Thesis, University of North Carolina at Chapel Hill (2012)

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599, USA

    Matthew J. Willis

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  1. Matthew J. Willis
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Correspondence to Matthew J. Willis.

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Contained in the author’s doctoral thesis written under the supervision of Robert A. Proctor.

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Willis, M.J. A Direct Way to Find the Right Key of a Semistandard Young Tableau. Ann. Comb. 17, 393–400 (2013). https://doi.org/10.1007/s00026-013-0187-4

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  • DOI: https://doi.org/10.1007/s00026-013-0187-4

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