Xiaoguang Ma
On elliptic Calogero-Moser systems for complex crystallographic reflection groups.
Thu, 03/25/2010 - 16:01 — SomNambulAuthors: Giovanni Felder, Xiaoguang Ma, Pavel Etingof, Alexander Veselov
Subjects: Quantum Algebra
AbstractTo every irreducible finite crystallographic reflection group (i.e., an
irreducible finite reflection group G acting faithfully on an abelian variety
X), we attach a family of classical and quantum integrable systems on X (with
meromorphic coefficients). These families are parametrized by G-invariant
functions of pairs (T,s), where T is a hypertorus in X (of codimension 1), and
s in G is a reflection acting trivially on T. If G is a real reflection group,
these families reduce to the known generalizations of elliptic Calogero-Moser
systems, but in the non-real case they appear to be new.Lecture notes on Cherednik algebras.
Tue, 01/05/2010 - 16:01 — SomNambulAuthors: Xiaoguang Ma, Pavel Etingof
Subjects: Representation Theory
AbstractThe present notes are based on a course on Cherednik algebras given by the
first author at MIT in the Fall of 2009. Their goal is to give an introduction
to Cherednik algebras, and to review the web of connections between them and
other mathematical objects.Quantum symmetric pairs and representations of double affine Hecke algebras of type $(C^\vee_n,C_n)$.
Mon, 08/24/2009 - 13:10 — SomNambulAuthors: David Jordan, Xiaoguang Ma
Subjects: Quantum Algebra
AbstractWe build representations of the affine and double affine braid groups and
Hecke algebras of type $(C^\vee_n,C_n)$, based upon the theory of quantum
symmetric pairs $(U,B)$. In the case $U=U_q(gl_N)$, our constructions provide a
quantization of the representations constructed by Etingof, Freund and Ma in
arXiv:0801.1530, and also a type $BC$ generalization of the results in
arXiv:0805.2766.- 11 comments
- login or register to post comments
User login
