# 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

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topGrantcharov, 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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