Crystal bases for the quantum queer superalgebra

Dimitar Grantcharov; Ji Hye Jung; Seok-Jin Kang; Masaki Kashiwara; Myungho Kim

Journal of the European Mathematical Society (2015)

  • Volume: 017, Issue: 7, page 1593-1627
  • ISSN: 1435-9855

Abstract

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In this paper, we develop the crystal basis theory for the quantum queer superalgebra U q ( 𝔮 ( n ) ) . We define the notion of crystal bases and prove the tensor product rule for U q ( 𝔮 ( n ) ) -modules in the category 𝒪 int ≥ 0 . Our main theorem shows that every U q ( 𝔮 ( n ) ) -module in the category 𝒪 int ≥ 0 has a unique crystal basis.

How to cite

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Grantcharov, Dimitar, et al. "Crystal bases for the quantum queer superalgebra." Journal of the European Mathematical Society 017.7 (2015): 1593-1627. <http://eudml.org/doc/277420>.

@article{Grantcharov2015,
abstract = {In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_q(\mathfrak \{q\}(n))$. We define the notion of crystal bases and prove the tensor product rule for $U_q(\mathfrak \{q\}(n))$-modules in the category $\mathcal \{O\}^\{\ge 0\}_\{\mathrm \{int\}\}$. Our main theorem shows that every $U_q(\mathfrak \{q\}(n))$-module in the category $\mathcal \{O\}^\{\ge 0\}_\{\mathrm \{int\}\}$ has a unique crystal basis.},
author = {Grantcharov, Dimitar, Jung, Ji Hye, Kang, Seok-Jin, Kashiwara, Masaki, Kim, Myungho},
journal = {Journal of the European Mathematical Society},
keywords = {quantum queer superalgebras; crystal bases; odd Kashiwara operators; quantum queer superalgebras; crystal bases; odd Kashiwara operators},
language = {eng},
number = {7},
pages = {1593-1627},
publisher = {European Mathematical Society Publishing House},
title = {Crystal bases for the quantum queer superalgebra},
url = {http://eudml.org/doc/277420},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Grantcharov, Dimitar
AU - Jung, Ji Hye
AU - Kang, Seok-Jin
AU - Kashiwara, Masaki
AU - Kim, Myungho
TI - Crystal bases for the quantum queer superalgebra
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 7
SP - 1593
EP - 1627
AB - In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_q(\mathfrak {q}(n))$. We define the notion of crystal bases and prove the tensor product rule for $U_q(\mathfrak {q}(n))$-modules in the category $\mathcal {O}^{\ge 0}_{\mathrm {int}}$. Our main theorem shows that every $U_q(\mathfrak {q}(n))$-module in the category $\mathcal {O}^{\ge 0}_{\mathrm {int}}$ has a unique crystal basis.
LA - eng
KW - quantum queer superalgebras; crystal bases; odd Kashiwara operators; quantum queer superalgebras; crystal bases; odd Kashiwara operators
UR - http://eudml.org/doc/277420
ER -

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