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Root system pattern avoidance, rational smoothness, and inversion arrangements

Student-Run Applied & Math Seminar

Speaker: William Slofstra, UC Davis
Location: 2112 MSB
Start time: Wed, Dec 4 2013, 12:10PM

A theorem of Lakshmibai-Sandhya states that smooth Schubert varieties in the flag variety of a vector space correspond to permutations which avoid two patterns. Billey and Postnikov introduced the notion of root-system pattern avoidance to extend this criterion to Schubert varieties of arbitrary type. Their criterion requires checking patterns in a finite number of spectral root systems. I will explain how to get a root-system pattern avoidance criterion for freeness of inversion hyperplane arrangements, and talk about some further problems in this area.