G. Benkart and D. Moon :
“Tensor product representations of Temperley–Lieb algebras and their centralizer algebras ,”
pp. 151–166
in
Topics in Young diagrams and representation theory
(6–9 November 2001, Kyoto ).
Edited by M. Kosuda .
Sūrikaisekikenkyūsho Kōkyūroku 1262 .
2002 .
Also published in Combinatorial and geometric representation theory (2003)
MR
1929395 incollection
People
BibTeX
@incollection {key1929395m,
AUTHOR = {Benkart, Georgia and Moon, Dongho},
TITLE = {Tensor product representations of {T}emperley--{L}ieb
algebras and their centralizer algebras},
BOOKTITLE = {Topics in {Y}oung diagrams and representation
theory},
EDITOR = {Kosuda, Masashi},
SERIES = {S\=urikaisekikenky\=usho K\=oky\=uroku},
NUMBER = {1262},
YEAR = {2002},
PAGES = {151--166},
NOTE = {(6--9 November 2001, Kyoto). Also published
in \textit{Combinatorial and geometric
representation theory} (2003). MR:1929395.},
ISSN = {1880-2818},
}
G. Benkart and D. Moon :
“Tensor product representations of Temperley–Lieb algebras and their centralizer algebras 31–49
in
Combinatorial and geometric representation theory
(22–26 October 2001, Seoul ).
Edited by S.-J. Kang and K.-H. Lee .
Contemporary Mathematics 325 .
American Mathematical Society (Providence, RI ),
2003 .
Also published in Topics in Young diagrams and representation theory (2002)
MR
1988984 Zbl
1031.17003 incollection
People
BibTeX
@incollection {key1988984m,
AUTHOR = {Benkart, Georgia and Moon, Dongho},
TITLE = {Tensor product representations of {T}emperley--{L}ieb
algebras and their centralizer algebras},
BOOKTITLE = {Combinatorial and geometric representation
theory},
EDITOR = {Kang, Seok-Jin and Lee, Kyu-Hwan},
SERIES = {Contemporary Mathematics},
NUMBER = {325},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2003},
PAGES = {31--49},
DOI = {10.1090/conm/325/05663},
NOTE = {(22--26 October 2001, Seoul). Also published
in \textit{Topics in Young diagrams
and representation theory} (2002). MR:1988984.
Zbl:1031.17003.},
ISSN = {0271-4132},
}
G. Benkart and D. Moon :
“Tensor product representations of Temperley–Lieb algebras and Chebyshev polynomials ,”
pp. 57–80
in
Representations of algebras and related topics
(15 July–10 August 2002, Toronto ).
Edited by R.-O. Buchweitz and H. Lenzing .
Fields Institute Communications 45 .
American Mathematical Society (Providence, RI ),
2005 .
To Professor Vlastimil Dlab with our best wishes on our seventieth birthday.
MR
2146240 Zbl
1179.17009 incollection
Abstract
People
BibTeX
The Brauer algebra \( B_k(n) \) determines the centralizer algebra of the action of the orthogonal group \( O_n \) on the \( k \) -fold tensor power \( V^{\otimes k} \) of its natural \( n \) -dimensional module \( V \) . As a subalgebra of the Brauer algebra, the Temperley–Lieb alebra \( TL_k(n) \) inherits an action on \( V^{\otimes k} \) . In this work, we investigate the centralizer algebra \( \mathcal{Z}_k(n) \) of the Temperley–Lieb algera on this tensor product space. We show that the dimesions of the irreducible \( \mathcal{Z}_k(n) \) -modules are related to vlaues of Chebyshev polynomials of the second kind. We determine the branching rule from \( B_k(n) \) to \( TL_k(n) \) using inverse Chebyshev relations.
@incollection {key2146240m,
AUTHOR = {Benkart, Georgia and Moon, Dongho},
TITLE = {Tensor product representations of {T}emperley--{L}ieb
algebras and {C}hebyshev polynomials},
BOOKTITLE = {Representations of algebras and related
topics},
EDITOR = {Buchweitz, Ragnar-Olaf and Lenzing,
Helmut},
SERIES = {Fields Institute Communications},
NUMBER = {45},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {2005},
PAGES = {57--80},
NOTE = {(15 July--10 August 2002, Toronto).
To Professor Vlastimil Dlab with our
best wishes on our seventieth birthday.
MR:2146240. Zbl:1179.17009.},
ISSN = {1069-5265},
ISBN = {9780821834152},
}
S. Cho, K.-C. Ha, Y.-O. Kim, and D. Moon :
“Key exchange protocol using matrix algebras and its analysis J. Korean Math. Soc.
42 : 6
(2005 ),
pp. 1287–1309 .
MR
2176265 Zbl
1083.94007 article
People
BibTeX
@article {key2176265m,
AUTHOR = {Cho, Soojin and Ha, Kil-Chan and Kim,
Young-One and Moon, Dongho},
TITLE = {Key exchange protocol using matrix algebras
and its analysis},
JOURNAL = {J. Korean Math. Soc.},
FJOURNAL = {Journal of the Korean Mathematical Society},
VOLUME = {42},
NUMBER = {6},
YEAR = {2005},
PAGES = {1287--1309},
DOI = {10.4134/JKMS.2005.42.6.1287},
NOTE = {MR:2176265. Zbl:1083.94007.},
ISSN = {0304-9914},
}
S. Cho, E.-K. Jung, and D. Moon :
“A hive-model proof of the second reduction formula of Littlewood–Richardson coefficients Ann. Comb.
15 : 2
(2011 ),
pp. 223–231 .
MR
2813512 Zbl
1233.05210 article
People
BibTeX
@article {key2813512m,
AUTHOR = {Cho, Soojin and Jung, Eun-Kyoung and
Moon, Dongho},
TITLE = {A hive-model proof of the second reduction
formula of {L}ittlewood--{R}ichardson
coefficients},
JOURNAL = {Ann. Comb.},
FJOURNAL = {Annals of Combinatorics},
VOLUME = {15},
NUMBER = {2},
YEAR = {2011},
PAGES = {223--231},
DOI = {10.1007/s00026-011-0091-8},
NOTE = {MR:2813512. Zbl:1233.05210.},
ISSN = {0218-0006},
}
G. Benkart and D. Moon :
“Planar rook algebras and tensor representations of \( \mathfrak{gl}(1|1) \) Comm. Algebra
41 : 7
(2013 ),
pp. 2405–2416 .
MR
3169400 Zbl
1269.05115 ArXiv
1201.2482 article
Abstract
People
BibTeX
We establish a connection between planar rook algebras and tensor representations \( \mathbf{V}^{\otimes k} \) of the natural two-dimensional representation \( \mathbf{V} \) of the general linear Lie superalgebra \( \mathfrak{gl}(1|1) \) . In particular, we show that the centralizer algebra \( \operatorname{E}_{\mathfrak{gl}(1|1)}(\mathbf{V}^{\otimes k}) \) is the planar rook algebra \( \mathbb{C}P_{k-1} \) for all \( k\geq 1 \) , and we exhibit an explicit decomposition of \( \mathbf{V}^{\otimes k} \) into irreducible \( \mathfrak{gl}(1|1) \) -modules. We obtain similar results for the quantum enveloping algebra \( \mathbf{U}_{\mathbf{q}}(\mathfrak{gl}(1|1)) \) and its natural two-dimensional module \( \mathbf{V}_{\mathbf{q}} \) .
@article {key3169400m,
AUTHOR = {Benkart, Georgia and Moon, Dongho},
TITLE = {Planar rook algebras and tensor representations
of \$\mathfrak{gl}(1|1)\$},
JOURNAL = {Comm. Algebra},
FJOURNAL = {Communications in Algebra},
VOLUME = {41},
NUMBER = {7},
YEAR = {2013},
PAGES = {2405--2416},
DOI = {10.1080/00927872.2012.658533},
NOTE = {ArXiv:1201.2482. MR:3169400. Zbl:1269.05115.},
ISSN = {0092-7872},
}
G. Benkart, S. Cho, and D. Moon :
“The combinatorics of \( \mathbf{A}_2 \) -webs ,”
Electron. J. Combin.
21 : 2
(2014 ).
Research Paper 2.25, 33 pages.
MR
3210659 Zbl
1300.05316 ArXiv
1312.1023 article
People
BibTeX
@article {key3210659m,
AUTHOR = {Benkart, Georgia and Cho, Soojin and
Moon, Dongho},
TITLE = {The combinatorics of \$\mathbf{A}_2\$-webs},
JOURNAL = {Electron. J. Combin.},
FJOURNAL = {Electronic Journal of Combinatorics},
VOLUME = {21},
NUMBER = {2},
YEAR = {2014},
NOTE = {Research Paper 2.25, 33 pages. ArXiv:1312.1023.
MR:3210659. Zbl:1300.05316.},
ISSN = {1077-8926},
}
G. Benkart and D. Moon :
“A Schur–Weyl duality approach to walking on cubes Ann. Comb.
20 : 3
(2016 ),
pp. 397–417 .
MR
3537911 Zbl
1347.05246 ArXiv
1409.8154 article
Abstract
People
BibTeX
@article {key3537911m,
AUTHOR = {Benkart, Georgia and Moon, Dongho},
TITLE = {A {S}chur--{W}eyl duality approach to
walking on cubes},
JOURNAL = {Ann. Comb.},
FJOURNAL = {Annals of Combinatorics},
VOLUME = {20},
NUMBER = {3},
YEAR = {2016},
PAGES = {397--417},
DOI = {10.1007/s00026-016-0311-3},
NOTE = {ArXiv:1409.8154. MR:3537911. Zbl:1347.05246.},
ISSN = {0218-0006},
}
