Gaetz, Christian Gao, Yibo
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Björner and Ekedahl (Ann Math (2) 170(2):799–817, 2009) prove that general intervals [e, w] in Bruhat order are “top-heavy”, with at least as many elements in the i-th corank as the i-th rank. Well-known results of Carrell (in: Algebraic groups and their generalizations: classical methods (University Park, PA, 1991), volume 56 of proceedings of sym...

Çineli, Erman Ginzburg, Viktor L. Gürel, Başak Z.
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We prove a variant of the Chance–McDuff conjecture for pseudo-rotations: under certain additional conditions, a closed symplectic manifold which admits a Hamiltonian pseudo-rotation must have deformed quantum product and, in particular, some non-zero Gromov–Witten invariants. The only assumptions on the manifold are that it is weakly monotone and t...

Nagpal, Rohit Sam, Steven V. Snowden, Andrew
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A major open problem in the theory of twisted commutative algebras (tca’s) is proving noetherianity of finitely generated tca’s. For bounded tca’s this is easy; in the unbounded case, noetherianity is only known for Sym(Sym2(C∞))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepa...

Heleodoro, Aron
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We construct a map from the prestack of Tate objects over a commutative ring k to the stack of Gm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {G}}_{\mathrm{...

Yom Din, Alexander
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I am grateful to D. Gaitsgory for pointing out the mistake.

Brundan, Jonathan Savage, Alistair Webster, Ben
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We show that any Abelian module category over the (degenerate or quantum) Heisenberg category satisfying suitable finiteness conditions may be viewed as a 2-representation over a corresponding Kac–Moody 2-category (and vice versa). This gives a way to construct Kac–Moody actions in many representation-theoretic examples which is independent of Rouq...

Calaque, Damien Gonzalez, Martin
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We construct a twisted version of the genus one universal Knizhnik–Zamolodchikov–Bernard (KZB) connection introduced by Calaque–Enriquez–Etingof, that we call the ellipsitomic KZB connection. This is a flat connection on a principal bundle over the moduli space of Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{...

Wilson, Jon
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It was shown by Fock and Goncharov (Dual Teichmüller and lamination spaces. Handbook of Teichmüller Theory, 2007), and Fomin et al. (Acta Math 201(1):83–146, 2008) that some cluster algebras arise from triangulated orientable surfaces. Subsequently, Dupont and Palesi (J Algebraic Combinatorics 42(2):429–472, 2015) generalised this construction to i...

Basu, Saugata Patel, Deepam
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In this article, we use cohomological techniques to obtain an algebraic version of Toda’s theorem in complexity theory valid over algebraically closed fields of arbitrary characteristic. This result follows from a general ‘connectivity’ result in cohomology. More precisely, given a closed subvariety X⊂Pn\documentclass[12pt]{minimal} \usepackage{ams...

Lu, Jiang-Hua Yu, Shizhuo
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Let G be a connected and simply connected complex semisimple Lie group. For a collection of homogeneous G-spaces G/Q, we construct a finite atlas ABS(G/Q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsid...