This volume is an outgrowth of the conference “Representation Theory of Alge-
braic Groups and Quantum Groups ’10” held at Nagoya University, Nagoya, Japan,
during the period August 2-6, 2010, as the 10th International conference hosted by
the Graduate School of Mathematics, Nagoya University.
This conference is the third one held in Japan under the same title. The first
one was held at Sophia Univeristy in Tokyo, in August of 2001, and the second
was held at Nagoya University, in June of 2006. This conference was planned
as a continuation of those precedent ones. The purpose of these conferences is
to focus on recent developments in the representation theory of algebraic groups
and quantum groups. The conference also aims to bring young researchers a good
opportunity for stimulating discussions with experts. During the conference, 22
lectures were delivered by invited speakers, which cover the topics such as modular
representations of algebraic groups and finite groups of Lie type, representations
of quantum groups and crystal bases, representations of aﬃne Lie algebras and
W -algebras, representations of Hecke algebras and Cherednik algebras, the theory
of cluster algebras and its applications to the representation theory.
This volume contains fourteen articles contributed by invited speakers of the
We are very grateful for the invited speakers for excellent lectures, for all the
participants for their participation with great enthusiasm, and in particular for
the contributors of the articles to this volume. We also thank the Grant-in-Aid
for Scientific Research by the Japan Society for the Promotion of Science for the
Last but not least, we wish to thank Ms. Kazuko Kozaki and other secretaries,
graduate students of the Graduate School of Mathematics, Nagoya Univeristy for
their dedicated support of the conference.