Yuri Bazlov
Link to Yuri Bazlov's home page
Research interests:
Representation theory and quantum algebra.
- Representation theory
- is a branch of mathematics
concerned with the question how to "realise"
abstract algebraic constructions by means of symmetries of some object
(e.g., by means of linear transformations of a vector space).
- Quantum algebra
- is a relatively young but very active field, which includes certain directions of research
in Hopf algebras, Lie theory, noncommutative ring theory, combinatorics, etc. Its scope roughly corresponds
to the scope of the
math.QA section
of arXiv.org.
Mathematical research in both fields is to a large extent inspired by
theoretical physics,
and it is therefore natural that many algebraic objects that
I study have origins in physics.
In particular, my research concerns
- Lie theory: Cherednik algebras, affine Hecke algebras, reflection/Coxeter groups, semisimple Lie algebras
- deformed and quantised rings of differential
operators
- braided categories, Nichols-Woronowicz algebras
Selected papers:
-
(with A. Berenstein) Cocycle twists and extensions of braided doubles,
submitted
[preprint version]
-
The Harish-Chandra isomorphism for Clifford algebras, submitted
[arXiv:0812.2059]
-
(with A. Berenstein)
Noncommutative Dunkl operators and braided Cherednik algebras,
Selecta Math. 14 (2009), no. 3-4, 325--372 [also arXiv:0806.0867]
-
(with A. Berenstein)
Braided doubles and rational Cherednik algebras,
Advances in Math. 220 (2009), no. 5, 1466--1530
-
Nichols-Woronowicz algebra model for Schubert calculus on Coxeter
groups,
J. Algebra
297 (2006), no. 2, 372--399
-
Graded multiplicities in the exterior algebra,
Advances in Math. 158
(2001), no. 2, 129--153