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Lie Group Quantum Mathematics Seminar

Imaginary root strings and Chevalley-Steinberg group commutators for hyperbolic Kac--Moody algebras

Lisa Carbone, Rutgers University and Institute for Advanced Study, School of Natural Sciences

Location:  zoom
Date & time: Friday, 12 March 2021 at 12:00PM - 1:00PM

Abstract Let L be a symmetrizable hyperbolic Kac--Moody algebra. We show that any root string in the direction of an imaginary root is infinite and we show that bi-infinite roots strings in the direction of an imaginary root can occur. For L hyperbolic of rank 2, we classify all the possible root strings that can occur. When L is also symmetric, we describe how root strings determine the Chevalley-Steinberg group commutators in a complete Kac--Moody group associated to L and we give a recursive method for determining them.

This is joint work with T. Coelho, J. Fonseca, J. Meng, S. H. Murray, F. Thurman and S. Zhu. This work arose from collaborative discussions in my graduate course "Topics in Algebra" in Spring 2020.

Zoom link
Meeting ID: 939 2146 5287
Passcode: 196884, the dimension of the weight 2 homogeneous
subspace of the moonshine module

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