Galkin's lower bound conjecture holds for the Grassmannian. Issue 2 (1st February 2020)

• Record Type: Journal Article
• Authors: Evans, La'Tier; Schneider, Lisa; Shifler, Ryan M.; Short, Laura; Warman, Stephanie
• Is Part Of: Communications in algebra. Volume 48:Issue 2(2020)
• Page Start: 857
• Page End: 865
• Publication Date: 2020-02-01
• Subjects: Algebraic geometry -- conjecture O -- quantum cohomology; Primary 14N35 -- Secondary 15B48 -- 14N15 -- 14M15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1663383
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let Gr ( k, n ) be the Grassmannian. The quantum multiplication by the first Chern class c 1 ( Gr ( k, n ) ) induces an endomorphism c ̂ 1 of the finite-dimensional vector space QH * ( Gr ( k, n ) ) | q = 1 specialized at q = 1. Our main result is a case that a conjecture by Galkin holds. It states that the largest real eigenvalue of c ̂ 1 is greater than or equal to dim Gr ( k, n ) +1 with equality if and only if Gr ( k, n ) = P n − 1 .