Title: INVARIANT THEORY OF CLASSICAL, QUANTUM AND SUPER GROUPS
Speaker: RUIBIN ZHANG
Time:
May 22（Friday）, 9:00--11:00
May 23（Saturday）, 09:00--11:00
May 27（Wednesday）, 19:00--21:00
May 29（Friday）, 14:00--16:00
Place: Room 1518, R&D Building
Abstract:
There has been significant progress in classical invariant theory in recent years through the introduction of the notion of quantum deformations, which has brought braid groups into the picture, the theory of braided tensor categories, which provides the natural framework for diagrammatic methods, and the theory of cellular algebras, which is well adapted to the study of non-semisimple representations.
We will discuss some of the classical results, explain new ideas, and describe some of the recent progress, particularly in the cases of supergroups and quantum groups. The lectures are based on the following papers:
(1) Gus Lehrer and Ruibin Zhang, “Strongly multiplicity free modules for Lie algebras and quantum groups”, J. Alg. 306 (2006), 138�174.
(2) Gus Lehrer, Hechun Zhang and Ruibin Zhang, “A quantum analogue of the first fundamental theorem of classical invariant theory”, Commun. Math. Physics, 301 (2011), 131-174.
(3) Gus Lehrer and Ruibin Zhang, “The second fundamental theorem of invariant theory for the orthogonal group”, Ann. Math. (2) 176 (2012), no. 3,
2031�2054.
(4) Gus Lehrer and Ruibin Zhang, “The Brauer category and invariant theory”, J. Europ. Math. Society, in press. arXiv:1207.5889
(5) Henning Andersen, Gus Lehrer and Ruibin Zhang, “Cellularity of certain quantum endomorphism algebras”, Pacific J. Math., in press. arXiv:1303.0984.
(6) Gus Lehrer and Ruibin Zhang, “The first fundamental theorem of invariant theory for the orthosymplectic supergroup”, arXiv:1401.7395.
(7) Gus Lehrer and Ruibin Zhang, “The second fundamental theorem of invariant theory for the orthosymplectic supergroup”, arXiv:1407.1058.
(8) Gus Lehrer and Ruibin Zhang, “Invariants of the orthosymplectic Lie superalgebra and the super Pfaffian”. Preprint, 2015.
(9) Gus Lehrer, Hechun Zhang and Ruibin Zhang, “The first fundamental theorem of invariant theory for quantum supergroups”, in preparation.
