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Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type An-1(1), Cn-1(1), A2n-2(2), Dn(2)
In this paper, we consider polyhedral realizations for crystal bases B ( λ ) of irreducible integrable highest weight modules of a quantized enveloping algebra U q ( g ) , where g is a classical affine Lie algebra of type A n - 1 ( 1 ) , C n - 1 ( 1 ) , A 2 n - 2 ( 2 ) or D n ( 2 ) . We will give ex...
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| Published in: | Letters in mathematical physics 2023-06, Vol.113 (3) |
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| Language: | English |
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| container_title | Letters in mathematical physics |
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| creator | Kanakubo, Yuki |
| description | In this paper, we consider polyhedral realizations for crystal bases
B
(
λ
)
of irreducible integrable highest weight modules of a quantized enveloping algebra
U
q
(
g
)
, where
g
is a classical affine Lie algebra of type
A
n
-
1
(
1
)
,
C
n
-
1
(
1
)
,
A
2
n
-
2
(
2
)
or
D
n
(
2
)
. We will give explicit forms of polyhedral realizations in terms of extended Young diagrams or Young walls that appear in the representation theory of quantized enveloping algebras of classical affine type. As an application, a combinatorial description of
ε
k
∗
functions on
B
(
∞
)
will be given. |
| doi_str_mv | 10.1007/s11005-023-01680-0 |
| format | article |
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B
(
λ
)
of irreducible integrable highest weight modules of a quantized enveloping algebra
U
q
(
g
)
, where
g
is a classical affine Lie algebra of type
A
n
-
1
(
1
)
,
C
n
-
1
(
1
)
,
A
2
n
-
2
(
2
)
or
D
n
(
2
)
. We will give explicit forms of polyhedral realizations in terms of extended Young diagrams or Young walls that appear in the representation theory of quantized enveloping algebras of classical affine type. As an application, a combinatorial description of
ε
k
∗
functions on
B
(
∞
)
will be given.</description><identifier>EISSN: 1573-0530</identifier><identifier>DOI: 10.1007/s11005-023-01680-0</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Complex Systems ; Geometry ; Group Theory and Generalizations ; Mathematical and Computational Physics ; Physics ; Physics and Astronomy ; Theoretical</subject><ispartof>Letters in mathematical physics, 2023-06, Vol.113 (3)</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-s1140-e793c2a531c6bf9def38936948201fdbe8daf17f403044f90ebeffca9b057aae3</cites><orcidid>0000-0001-5322-5711</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Kanakubo, Yuki</creatorcontrib><title>Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type An-1(1), Cn-1(1), A2n-2(2), Dn(2)</title><title>Letters in mathematical physics</title><addtitle>Lett Math Phys</addtitle><description>In this paper, we consider polyhedral realizations for crystal bases
B
(
λ
)
of irreducible integrable highest weight modules of a quantized enveloping algebra
U
q
(
g
)
, where
g
is a classical affine Lie algebra of type
A
n
-
1
(
1
)
,
C
n
-
1
(
1
)
,
A
2
n
-
2
(
2
)
or
D
n
(
2
)
. We will give explicit forms of polyhedral realizations in terms of extended Young diagrams or Young walls that appear in the representation theory of quantized enveloping algebras of classical affine type. As an application, a combinatorial description of
ε
k
∗
functions on
B
(
∞
)
will be given.</description><subject>Complex Systems</subject><subject>Geometry</subject><subject>Group Theory and Generalizations</subject><subject>Mathematical and Computational Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Theoretical</subject><issn>1573-0530</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNo1kM9KAzEQxoMgWKsv4CnHCkYnyW5391jqXyjoQc9LsjtpU7ZJSVKkPoZPbGz19H3DfDPD_Ai54nDLAaq7yLOUDIRkwKc1MDghI15WuSwlnJHzGNeQg6KEEfl-88N-hX1QAw2oBvulkvUuUuMD7cI-ptzQKmKk3lDrEi6D0gPSlV2uMCb6idkkuvH9bsgh5Xra-Y22TiUfbB72eo1dOoyn_RbpzDE-4dc3dP5vZsIxMRHZ3bssF-TUqCHi5Z-Oycfjw_v8mS1en17mswXLDxbAsGpkJ1QpeTfVpunRyLqR06aoBXDTa6x7ZXhlCpBQFKYB1GhMpxoNZaUUyjGRx71xG6xbYmjXfhdcPtlyaH9RtkeUbUbZHlC2IH8AYENolA</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Kanakubo, Yuki</creator><general>Springer Netherlands</general><scope/><orcidid>https://orcid.org/0000-0001-5322-5711</orcidid></search><sort><creationdate>20230601</creationdate><title>Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type An-1(1), Cn-1(1), A2n-2(2), Dn(2)</title><author>Kanakubo, Yuki</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-s1140-e793c2a531c6bf9def38936948201fdbe8daf17f403044f90ebeffca9b057aae3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Complex Systems</topic><topic>Geometry</topic><topic>Group Theory and Generalizations</topic><topic>Mathematical and Computational Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kanakubo, Yuki</creatorcontrib><jtitle>Letters in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kanakubo, Yuki</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type An-1(1), Cn-1(1), A2n-2(2), Dn(2)</atitle><jtitle>Letters in mathematical physics</jtitle><stitle>Lett Math Phys</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>113</volume><issue>3</issue><eissn>1573-0530</eissn><abstract>In this paper, we consider polyhedral realizations for crystal bases
B
(
λ
)
of irreducible integrable highest weight modules of a quantized enveloping algebra
U
q
(
g
)
, where
g
is a classical affine Lie algebra of type
A
n
-
1
(
1
)
,
C
n
-
1
(
1
)
,
A
2
n
-
2
(
2
)
or
D
n
(
2
)
. We will give explicit forms of polyhedral realizations in terms of extended Young diagrams or Young walls that appear in the representation theory of quantized enveloping algebras of classical affine type. As an application, a combinatorial description of
ε
k
∗
functions on
B
(
∞
)
will be given.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11005-023-01680-0</doi><orcidid>https://orcid.org/0000-0001-5322-5711</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 1573-0530 |
| ispartof | Letters in mathematical physics, 2023-06, Vol.113 (3) |
| issn | 1573-0530 |
| language | eng |
| recordid | cdi_springer_journals_10_1007_s11005_023_01680_0 |
| source | Springer Nature |
| subjects | Complex Systems Geometry Group Theory and Generalizations Mathematical and Computational Physics Physics Physics and Astronomy Theoretical |
| title | Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type An-1(1), Cn-1(1), A2n-2(2), Dn(2) |
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