涩里番

罢颈迟濒别:听Coxeter and Schubert combinatorics of聽渭-Involutions

础产蝉迟谤补肠迟:听The variety of complete quadrics is the wonderful compactification of聽GLn/On聽and admits a cell decomposition into Borel orbits indexed by combinatorial objects called聽渭鈥搃nvolutions. We study Coxeter鈥搕heoretic properties of聽渭鈥搃nvolutions with results including a combinatorial description for their atoms, an exchange lemma, and transposition-like operators that characterize their Bruhat order. The corresponding orbit closures can be realized inside the flag variety. In this setting, we study the cohomology representatives of these orbits, which are, up to a scalar, the聽渭鈥搃nvolution Schubert polynomials. We expand聽渭鈥搃nvolution Schubert polynomials as a multiplicity-free sum of聽谓鈥搃nvolution Schubert polynomials when聽谓聽refines聽渭聽and provide recurrences analogous to Monk鈥檚 rule for Schubert polynomials. This is joint work with Zachary Hamaker.

尝辞肠补迟颈辞苍:听PK-4323 of UQAM鈥檚 Pr茅sident-Kennedy Building.