On rectangular Kronecker coefficients
Laurent Manivel
DOI: 10.1007/s10801-010-0240-x
Abstract
We show that rectangular Kronecker coefficients stabilize when the lengths of the sides of the rectangle grow, and we give an explicit formula for the limit values in terms of invariants of \mathfrak s l n \mathfrak{s}l_{n}.
Pages: 153–162
Keywords: keywords Kronecker coefficient; invariant theory; symmetric group; special linear group; tensor product
Full Text: PDF
References
1. Benkart, G., Doty, S.: Derangements and tensor powers of adjoint modules for sln. J. Algebr. Comb. 16(1), 31-42 (2002)
2. Brion, M.: Stable properties of plethysm: on two conjectures of Foulkes. Manuscr. Math. 80(4), 347- 371 (1993)
3. Buergisser, P., Landsberg, J.M., Manivel, L., Weyman, J.: An overview of mathematical issues arising in the geometric complexity theory approach to VP vs VNP. arXiv
4. Formanek, E.: The invariants of n \times n matrices. In: Invariant Theory. Lecture Notes in Math., vol. 1278, pp. 18-43. Springer, Berlin (1987)
5. Garsia, A., Wallach, N., Xin, G., Zabrocki, M.: Kronecker coefficients via symmetric functions and constant term identities. Preprint (2008)
6. Howe, R.: Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond. In: The Schur Lectures (1992) (Tel Aviv). Israel Math. Conf. Proc., vol. 8, pp. 1-182. Bar-Ilan Univ., Ramat Gan (1995)
7. James, G., Kerber, A.: The Representation Theory of the Symmetric Group. Encyclopedia of Mathematics and its Applications, vol.
16. Addison-Wesley, Reading (1981)
8. Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2nd edn. Oxford University Press, Ox- ford (1995)
9. Manivel, L.: A note on certain Kronecker coefficients. Proc. Am. Math. Soc. 138, 1-7 (2010). arXiv:
10. Procesi, C.: Lie Groups, An Approach Through Invariants and Representations. Universitext. Springer, Berlin (2007)
11. Vallejo, E.: A stability property for coefficients in Kronecker products of complex Sn characters. Electron. J. Comb. 16(1) (2009), Note 22, 8 pp.
2. Brion, M.: Stable properties of plethysm: on two conjectures of Foulkes. Manuscr. Math. 80(4), 347- 371 (1993)
3. Buergisser, P., Landsberg, J.M., Manivel, L., Weyman, J.: An overview of mathematical issues arising in the geometric complexity theory approach to VP vs VNP. arXiv
4. Formanek, E.: The invariants of n \times n matrices. In: Invariant Theory. Lecture Notes in Math., vol. 1278, pp. 18-43. Springer, Berlin (1987)
5. Garsia, A., Wallach, N., Xin, G., Zabrocki, M.: Kronecker coefficients via symmetric functions and constant term identities. Preprint (2008)
6. Howe, R.: Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond. In: The Schur Lectures (1992) (Tel Aviv). Israel Math. Conf. Proc., vol. 8, pp. 1-182. Bar-Ilan Univ., Ramat Gan (1995)
7. James, G., Kerber, A.: The Representation Theory of the Symmetric Group. Encyclopedia of Mathematics and its Applications, vol.
16. Addison-Wesley, Reading (1981)
8. Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2nd edn. Oxford University Press, Ox- ford (1995)
9. Manivel, L.: A note on certain Kronecker coefficients. Proc. Am. Math. Soc. 138, 1-7 (2010). arXiv:
10. Procesi, C.: Lie Groups, An Approach Through Invariants and Representations. Universitext. Springer, Berlin (2007)
11. Vallejo, E.: A stability property for coefficients in Kronecker products of complex Sn characters. Electron. J. Comb. 16(1) (2009), Note 22, 8 pp.
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