This article is cited in 1 scientific paper (total in 1 paper)
Dual perfect bases and dual perfect graphs
Byeong Hoon Kahnga, Seok-Jin Kangab, Masaki Kashiwaraac, Uni Rinn Suhb
a Department of Mathematical Sciences, Seoul National University, 599 Gwanak-Ro, Seoul 151-747, Korea
b Research Institute of Mathematics, Seoul National University, 599 Gwanak-Ro, Seoul 151-747, Korea
c Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
We introduce the notion of dual perfect bases and dual perfect graphs. We show that every integrable highest weight module $V_q(\lambda)$ over a quantum generalized Kac–Moody algebra $U_q(\mathfrak g)$ has a dual perfect basis and its dual perfect graph is isomorphic to the crystal $B(\lambda)$. We also show that the negative half $U_q^-(\mathfrak g)$ has a dual perfect basis whose dual perfect graph is isomorphic to the crystal $B(\infty)$. More generally, we prove that all the dual perfect graphs of a given dual perfect space are isomorphic as abstract crystals. Finally, we show that the isomorphism classes of finitely generated graded projective indecomposable modules over a Khovanov–Lauda–Rouquier algebra and its cyclotomic quotients form dual perfect bases for their Grothendieck groups.
Key words and phrases:
perfect basis, dual perfect basis, upper global basis, lower global basis.
Received: May 9, 2014
Byeong Hoon Kahng, Seok-Jin Kang, Masaki Kashiwara, Uni Rinn Suh, “Dual perfect bases and dual perfect graphs”, Mosc. Math. J., 15:2 (2015), 319–335
Citation in format AMSBIB
\by Byeong~Hoon~Kahng, Seok-Jin~Kang, Masaki~Kashiwara, Uni~Rinn~Suh
\paper Dual perfect bases and dual perfect graphs
\jour Mosc. Math.~J.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
J. Brundan, N. Davidson, “Categorical actions and crystals”, Categorification and Higher Representation Theory, Contemporary Mathematics, 683, eds. A. Beliakova, A. Lauda, Amer. Math. Soc., 2017, 105+
|Number of views:|