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Mosc. Math. J., 2015, Volume 15, Number 2, Pages 319–335 (Mi mmj561)  

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

Abstract: 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.

DOI: https://doi.org/10.17323/1609-4514-2015-15-2-319-335

Full text: http://www.mathjournals.org/.../2015-015-002-008.html
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Bibliographic databases:

MSC: 20G42
Received: May 9, 2014
Language:

Citation: 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
\Bibitem{KahKanKas15}
\by Byeong~Hoon~Kahng, Seok-Jin~Kang, Masaki~Kashiwara, Uni~Rinn~Suh
\paper Dual perfect bases and dual perfect graphs
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 2
\pages 319--335
\mathnet{http://mi.mathnet.ru/mmj561}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-2-319-335}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427426}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000361607300008}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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+  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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