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Log-modular quantum groups at even roots of unity

Cris Negron, MIT
Tuesday, May 21, 2019 - 2:30pm
PDL C-36

I will discuss recent work on constructing small quantum groups at even order roots of unity.  By a small quantum group we mean a finite-dimensional quasitriangular (quasi-)Hopf algebra which is associated to an algebraic group \$\mathbb{G}\$ and choice of parameter \$q\in\mathbb{C}^\times\$, in a formal way.  Our work is motivated by recent conjectures which propose a strong relationship between quantum groups at even order parameters and ``logarithmic" conformal field theories.  I will explain this quantum group--CFT conjecture in type \$A_1\$ (i.e.\ for \$SL_2(\mathbb{C})\$), the precise problems that arise in attempting to define quantum groups at even order \$q\$, and our general method for overcoming these problems.  Of course, I will also explain what a quantum group actually is.

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