A canonical basis in general may refer to various distinguished or special bases of algebraic structures, or their underlying vector spaces. This entry is however about a rather involved theory of canonical bases of representations in Lie theory which has been discovered first in the quantum group context.
Fundamental works started with Lusztig and the dual case by Kashiwara
George Lusztig, Canonical bases arising from quantized enveloping algebras, J. Am. Math. Soc. 3, 447–498 (1990) doi
George Lusztig, Canonical bases in tensor products. Proc. Natl. Acad. Sci. 89 (1992) 8177–8179 doi
Masaki Kashiwara, On crystal bases of the -analogue of universal enveloping algebras Duke Math. J. 63, 456–516 (1991) doi
Masaki Kashiwara, Crystal bases of modified quantized enveloping algebra, Duke Math. J. 73 (1994) 383–413 doi
George Lusztig, Canonical bases and Hall algebras, In: Representation Theories and Algebraic Geometry
(Montreal, PQ, 1997), 365–399, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 514. Kluwer (1998)
Arkady Berenstein, J. Greenstein, Canonical bases of quantum Schubert cells and their symmetries, Sel. Math. New Ser. 23, 2755–2799 (2017) doi
Created on October 11, 2024 at 15:01:47. See the history of this page for a list of all contributions to it.