论文信息 - A study of the representations supported by the orbit closure of the determinant

A study of the representations supported by the orbit closure of the determinant

Abstract We show the existence of a large family of representations supported by the orbit closure of the determinant. However, the validity of our result is based on the validity of the celebrated ‘Latin square conjecture’ due to Alon and Tarsi or, more precisely, on the validity of an equivalent ‘column Latin square conjecture’ due to Huang and Rota.

Shrawan Kumar | Shrawan Kumar

[1] Ketan Mulmuley,et al. Geometric Complexity Theory II: Towards Explicit Obstructions for Embeddings among Class Varieties , 2006, SIAM J. Comput..

[2] R. Goodman,et al. Symmetry, Representations, and Invariants , 2009 .

[3] Noga Alon,et al. Colorings and orientations of graphs , 1992, Comb..

[4] Roger Howe,et al. (GLn, GLm)-duality and symmetric plethysm , 1987 .

[5] J. M. Landsberg,et al. An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to VP≠VNP , 2009, SIAM J. Comput..

[6] Matthias Christandl,et al. Nonvanishing of Kronecker coefficients for rectangular shapes , 2009, 0910.4512.

[7] Ketan Mulmuley,et al. Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems , 2002, SIAM J. Comput..

[8] Gian-Carlo Rota,et al. On the relations of various conjectures on Latin squares and straightening coefficients , 1994, Discret. Math..

[9] Arthur A. Drisko. On the Number of Even and Odd Latin Squares of Orderp+1 , 1997 .

[10] Shrawan Kumar,et al. Geometry of orbits of permanents and determinants , 2010, 1007.1695.

[11] David G. Glynn,et al. The Conjectures of Alon--Tarsi and Rota in Dimension Prime Minus One , 2010, SIAM J. Discret. Math..

[12] Leslie G. Valiant,et al. Completeness classes in algebra , 1979, STOC.

[13] B. Kostant. On Macdonald's η-function formula, the Laplacian and generalized exponents , 1976 .