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The canonical basis of the quantum adjoint representation. (English) Zbl 1422.17019
Summary: We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
20G42 Quantum groups (quantized function algebras) and their representations
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[1] C. Chevalley, Sur certains groupes simples, Tohoku Math. J., 7 (1955), 14–66. Zbl 0066.01503 MR 73602 · Zbl 0066.01503
[2] M. Kashiwara, On crystal bases of the q-analogue of universal enveloping algebras, Duke Math. J., 63 (1991), 465–516.Zbl 0739.17005 MR 1115118 · Zbl 0739.17005
[3] G. Lusztig, On quantum groups, J. Alg., 131 (1990), 466–475.Zbl 0698.16007 MR 1058558 · Zbl 0698.16007
[4] G. Lusztig, Quantum groups at roots of 1, Geom. Ded., 35 (1990), 89–114.Zbl 0714.17013 MR 1066560 · Zbl 0714.17013
[5] G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc., 3 (1990), 447–498.Zbl 0703.17008 MR 1035415 · Zbl 0703.17008
[6] G. Lusztig, Introduction to quantum groups, Progr. in Math., 110, Birkhäuser, Boston, 1993.Zbl 0788.17010 MR 1227098 · Zbl 0788.17010
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