Nonvanishing of Kronecker coefficients for rectangular shapes

Advances in Mathematics

Volumn 227, Issue 5, 2011, Pages 2082-2091

  Bürgisser, Peter ^a   Christandl, Matthias ^b   Ikenmeyer, Christian ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

^b ETH ZURICH   (Switzerland)

Author keywords

Geometric complexity theory; Kronecker coefficients; Quantum information theory; Quantum marginal problem

Indexed keywords

EID: 79956362053     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2011.04.012     Document Type: Article

References (20)

1. Bürgisser P., Christandl M., Ikenmeyer C. Even partitions in plethysms. J. Algebra 2011, 328:322-329.
2. Bürgisser P., Clausen M., Shokrollahi M.A. Algebraic Complexity Theory. Grundlehren Math. Wiss. 1997, vol. 315. Springer-Verlag, Berlin, with the collaboration of Thomas Lickteig.
3. Bürgisser P., Landsberg J., Manivel L., Weyman J. An overview of mathematical issues arising in the geometric complexity theory approach to VP≠VNP arxiv:0907.2850v2.
4. Christandl M., Harrow A., Mitchison G. On nonzero Kronecker coefficients and what they tell us about spectra. Comm. Math. Phys. 2007, 270:575-585.
5. Christandl M., Mitchison G. The spectra of density operators and the Kronecker coefficients of the symmetric group. Comm. Math. Phys. 2006, 261:789-797.
6. Christandl M., Winter A. Uncertainty, monogamy, and locking of quantum correlations. IEEE Trans. Inform. Theory 2005, 51:3159-3165.
7. Franz M. Moment polytopes of projective G-varieties and tensor products of symmetric group representations. J. Lie Theory 2002, 12:539-549.
8. Fulton W., Harris J. Representation Theory. Grad. Texts in Math. 1991, vol. 129. Springer-Verlag, New York.
9. Keyl M., Werner R. Estimating the spectrum of a density operator. Phys. Rev. A 2001, 64:052311.
10. Klyachko A.A. Stable bundles, representation theory and Hermitian operators. Selecta Math. (N.S.) 1998, 4:419-445.
11. Klyachko A. Quantum marginal problem and representations of the symmetric group arxiv:quant-ph/0409113v1.
12. Knutson A., Tao T. The honeycomb model of GLn(C) tensor products. I, Proof of the saturation conjecture. J. Amer. Math. Soc. 1999, 12:1055-1090.
13. Landsberg J.M., Manivel L. On the ideals of secant varieties of Segre varieties. Found. Comput. Math. 2004, 4:397-422.
14. Manivel L. Applications de Gauss et pléthysme. Ann. Inst. Fourier (Grenoble) 1997, 47:715-773.
15. Mulmuley K.D., Sohoni M. Geometric complexity theory. I, An approach to the P vs. NP and related problems. SIAM J. Comput. 2001, 31:496-526.
16. Mulmuley K.D., Sohoni M. Geometric complexity theory. II, Towards explicit obstructions for embeddings among class varieties. SIAM J. Comput. 2008, 38:1175-1206.
17. Stanley R.P. Enumerative Combinatorics. Vol. 2. Cambridge Stud. Adv. Math. 1999, vol. 62. Cambridge University Press, Cambridge.
18. Stanley R.P. Positivity problems and conjectures in algebraic combinatorics. Mathematics: Frontiers and Perspectives 2000, 295-319. Amer. Math. Soc., Providence, RI.
19. Valiant L.G. Completeness classes in algebra. Conference Record of the Eleventh Annual ACM Symposium on Theory of Computing 1979, 249-261. ACM, New York.
20. Valiant L.G. Reducibility by algebraic projections. Enseign. Math. (2) 1982, 28:253-268.