TY - JOUR
T1 - Quantum Twist Maps and Dual Canonical Bases
AU - Kimura, Yoshiyuki
AU - Oya, Hironori
N1 - Funding Information:
The work of the first author was supported by JSPS Grant-in-Aid for Scientific Research (S) 24224001. The work of the second author was supported by Grant-in-Aid for JSPS Fellows (No. 15J09231) and the Program for Leading Graduate Schools, MEXT, Japan.
Publisher Copyright:
© 2017, Springer Science+Business Media B.V.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the “reverse” lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors.
AB - In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the “reverse” lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors.
KW - Dual canonical bases
KW - Poincaré-Birkhoff-Witt type bases
KW - Quantized universal enveloping algebras
KW - Quantum T-systems
KW - Quantum twist maps
KW - Unipotent quantum minors
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U2 - 10.1007/s10468-017-9729-5
DO - 10.1007/s10468-017-9729-5
M3 - Article
AN - SCOPUS:85028298325
SN - 1386-923X
VL - 21
SP - 589
EP - 604
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 3
ER -