Quantum enveloping algebras and the q-deformed Fock space
Student No.:50
Time:Monday, 15:10-17:00, 2017-2-27~2017-6-12
Instructor:Bangming Deng  [Tsinghua University]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-2-27
Ending Date:2017-6-12



The q-deformed Fock space was introduced by Hayashi and its canonical basis was defined by Leclerc and Thibon. It turns out that this canonical basis has many important applications in representation theory.

This course gives a brief introduction on the q-deformed Fock space and its canonical basis in terms of Hall algebras of linear and cyclic quivers. The corresponding quantum enveloping algebras are of type sl∞ and of affine type sln and gln.  


Main references: 

S. Ariki, Representations of quantum algebras and combinatorics of

Young tableaux, University Lecture Series, 26. American Mathematical Society, Providence, RI, 2002.

B. Leclerc and J.-Y. Thibon, Canonical bases of q-deformed Fock spaces, Internat. Math. Res. Notices 1996, 447-456.

M. Varagnolo and E. Vasserot, On the decomposition matrices of the quantized Schur algebra, Duke Math. J. 100 (1999), 267-297.