Vandermonde determinantal ideals
DOI:
https://doi.org/10.7146/math.scand.a-114906Abstract
We show that the ideal generated by maximal minors (i.e., $k+1$-minors) of a $(k+1) \times n$ Vandermonde matrix is radical and Cohen-Macaulay. Note that this ideal is generated by all Specht polynomials with shape $(n-k,1, …,1)$.
References
Fröberg, R. and Shapiro, B., On Vandermonde varieties, Math. Scand. 119 (2016), no. 1, 73–91. https://doi.org/10.7146/math.scand.a-24185
Harima, T., Maeno, T., Morita, H., Numata, Y., Wachi, A., and Watanabe, J., The Lefschetz properties, Lecture Notes in Mathematics, vol. 2080, Springer, Heidelberg, 2013. https://doi.org/10.1007/978-3-642-38206-2
Miró-Roig, R. M., A note on the multiplicity of determinantal ideals, J. Algebra 299 (2006), no. 2, 714–724. https://doi.org/10.1016/j.jalgebra.2005.05.017
Miró-Roig, R. M., Determinantal ideals, Progress in Mathematics, vol. 264, Birkhäuser Verlag, Basel, 2008.
Sagan, B. E., The symmetric group: representations, combinatorial algorithms, and symmetric functions, second ed., Graduate Texts in Mathematics, vol. 203, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4757-6804-6
Watanabe, J. and Yanagawa, K., On Specht ideals, in preparation.
Harima, T., Maeno, T., Morita, H., Numata, Y., Wachi, A., and Watanabe, J., The Lefschetz properties, Lecture Notes in Mathematics, vol. 2080, Springer, Heidelberg, 2013. https://doi.org/10.1007/978-3-642-38206-2
Miró-Roig, R. M., A note on the multiplicity of determinantal ideals, J. Algebra 299 (2006), no. 2, 714–724. https://doi.org/10.1016/j.jalgebra.2005.05.017
Miró-Roig, R. M., Determinantal ideals, Progress in Mathematics, vol. 264, Birkhäuser Verlag, Basel, 2008.
Sagan, B. E., The symmetric group: representations, combinatorial algorithms, and symmetric functions, second ed., Graduate Texts in Mathematics, vol. 203, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4757-6804-6
Watanabe, J. and Yanagawa, K., On Specht ideals, in preparation.
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Published
2019-10-19
How to Cite
Watanabe, J., & Yanagawa, K. (2019). Vandermonde determinantal ideals. MATHEMATICA SCANDINAVICA, 125(2), 179–184. https://doi.org/10.7146/math.scand.a-114906
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