The next CART seminar is scheduled for Sep. 18 (Fri), 10:00-11:00 in Korea time (9:00-10:00 in Beijing). 

Speaker: Andrew Hardt (Towson University, USA)

Title: GL-multiplicities of type A quiver loci

Abstract: The space of representations of a quiver admits an orbit structure via change of basis. When the quiver is type A, the orbit closures are described by rank conditions. These varieties generalize classical degeneracy loci. Their equations are understood through work of Zelevinsky and Kinser–Rajchgot, and their cohomology classes and K-polynomials have been computed by many authors, including Buch–Fulton, Knutson–Miller–Shimozono, Buch–Rimányi and Kinser–Knutson–Rajchgot.  

The coordinate ring of a quiver orbit closure is a rational representation of a product of general linear groups. In the special case of varieties of complexes, its irreducible decomposition is implicit in work of De Concini and Strickland. In joint work with Ian Cavey and Alexander Yong, we give a positive combinatorial rule for this decomposition, valid for all type A orbit closures in every orientation. Our rule is in terms of nonnegative integer matrices satisfying admissibility conditions corresponding to the rank conditions of the orbit closure. We put a crystal structure on these matrices, using the combinatorics of Stembridge's rational tableaux, and the irreducible multiplicities are counted by the highest weight admissible matrices.

You can join the seminar via the following

Zoom link: https://kias-re-kr.zoom.us/j/86352829715?pwd=KBrb6UvVv1myhwDmE7Xm59UUGsyKia.1

Meeting ID: 863 5282 9715

Password: 264696

Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/).

Looking forward to seeing you at the seminar!

Best regards,

Sin-Myung Lee