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Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
noncommuting variables related Hopf algebras
2015/8/14
We identify two seemingly disparate structures: supercharacters, a useful way of doing
Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite
field, and th...
Transitive Lie algebras of vector fields---an overview
Transitive Lie algebras vector fields Differential Geometry
2011/9/6
Abstract: This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary diffe...
A Brylinski filtration for affine Kac-Moody algebras
Brylinski filtration affine Kac-Moody algebras
2011/1/20
Braverman and Finkelberg have recently proposed a conjectural analogue of the geometric Satake isomorphism for untwisted affine Kac-Moody groups.
Logarithmic tensor category theory for generalized modules for a conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules
Logarithmic tensor category theory for generalized modules conformal vertex algebra Introduction strongly graded algebras generalized modules
2011/2/23
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra.
We show that for any fixed point P0 on a Riemann surface the distinct realizations of cocycles in H1(,O) correspond to the natural appearances of the standard Heisenberg vertex operator algebra (P0...
Remarks on Cyclotomic and Degenerate Cyclotomic BMW Algebras
Degenerate Cyclotomic BMW Algebras math
2010/11/19
We relate the structure of cyclotomic and degenerate cyclotomic BMW algebras, for arbitrary parameter values, to that for admissible parameter values. In particular, we show that these algebras are ce...
Direct Construction of Grassmann, Clifford and Geometric Algebras
Direct Construction of Grassmann Clifford and Geometric Algebras
2010/11/22
This is a simple way rigorously to construct Grassmann, Clifford and Geometric Algebras, allowing degenerate bilinear forms, infinite dimension, using fields or certain modules (characteristic 2 with ...
Representations of Affine and Toroidal Lie Algebras
Representations of Affine Toroidal Lie Algebras
2010/12/1
We discuss the category I of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties.