Abstract
We introduce a new class of bases for quantized universal enveloping algebras Uq(g) and other doubles attached to semisimple and Kac–Moody Lie algebras. These bases contain dual canonical bases of upper and lower halves of Uq(g) and are invariant under many symmetries including all Lusztig's symmetries if g is semisimple. It also turns out that a part of a double canonical basis of Uq(g) spans its center and consists of higher Casimirs which suggests physical applications.
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