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Schur Polynomials and The Yang-Baxter Equation
We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map from to End , where V is a two-dimensional vector space such that if then R 12 ( g ) R 13 ( gh ) R 23 ( h ) = R 23 ( h ) R 13 ( gh ) R 12 ( g ). Here R i j denotes R appli...
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| Published in: | Communications in mathematical physics 2011-12, Vol.308 (2), p.281-301 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c384t-366dc6aa361800dd26bef9a4eba007cc9c820b9e963e5605a8d9707e4f6ecf3c3 |
| container_end_page | 301 |
| container_issue | 2 |
| container_start_page | 281 |
| container_title | Communications in mathematical physics |
| container_volume | 308 |
| creator | Brubaker, Ben Bump, Daniel Friedberg, Solomon |
| description | We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map
from
to End
, where
V
is a two-dimensional vector space such that if
then
R
12
(
g
)
R
13
(
gh
)
R
23
(
h
) =
R
23
(
h
)
R
13
(
gh
)
R
12
(
g
). Here
R
i
j
denotes
R
applied to the
i
,
j
components of
. The image of this map consists of matrices whose nonzero coefficients
a
1
,
a
2
,
b
1
,
b
2
,
c
1
,
c
2
are the Boltzmann weights for the non-field-free six-vertex model, constrained to satisfy
a
1
a
2
+
b
1
b
2
−
c
1
c
2
= 0. This is the exact center of the disordered regime, and is contained within the free fermionic eight-vertex models of Fan and Wu. As an application, we show that with boundary conditions corresponding to integer partitions
λ
, the six-vertex model is exactly solvable and equal to a Schur polynomial
s
λ
times a deformation of the Weyl denominator. This generalizes and gives a new proof of results of Tokuyama and Hamel and King. |
| doi_str_mv | 10.1007/s00220-011-1345-3 |
| format | article |
| fullrecord | <record><control><sourceid>pascalfrancis_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s00220_011_1345_3</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>24765431</sourcerecordid><originalsourceid>FETCH-LOGICAL-c384t-366dc6aa361800dd26bef9a4eba007cc9c820b9e963e5605a8d9707e4f6ecf3c3</originalsourceid><addsrcrecordid>eNp9j7tOwzAUhi0EEqXwAGxZGF2OL3HiEapSkCqBRBmYrBPHaVOlTrFbib49roIYmc7w385HyC2DCQMo7iMA50CBMcqEzKk4IyMmBaegmTonIwAGVCimLslVjBsA0FypEZm82_UhZG99d_T9tsUuZujrbLl22Sf6FX3E770L2ezrgPu299fkokked_N7x-TjabacPtPF6_xl-rCgVpRyn4ZUbRViGiwB6pqryjUapaswPWuttiWHSjuthMsV5FjWuoDCyUY52wgrxoQNvTb0MQbXmF1otxiOhoE5AZsB2CRgcwI2ImXuhswOo8WuCehtG_-CXBYql4IlHx98MUl-5YLZ9IfgE84_5T9UVGR5</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Schur Polynomials and The Yang-Baxter Equation</title><source>Springer Link</source><creator>Brubaker, Ben ; Bump, Daniel ; Friedberg, Solomon</creator><creatorcontrib>Brubaker, Ben ; Bump, Daniel ; Friedberg, Solomon</creatorcontrib><description>We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map
from
to End
, where
V
is a two-dimensional vector space such that if
then
R
12
(
g
)
R
13
(
gh
)
R
23
(
h
) =
R
23
(
h
)
R
13
(
gh
)
R
12
(
g
). Here
R
i
j
denotes
R
applied to the
i
,
j
components of
. The image of this map consists of matrices whose nonzero coefficients
a
1
,
a
2
,
b
1
,
b
2
,
c
1
,
c
2
are the Boltzmann weights for the non-field-free six-vertex model, constrained to satisfy
a
1
a
2
+
b
1
b
2
−
c
1
c
2
= 0. This is the exact center of the disordered regime, and is contained within the free fermionic eight-vertex models of Fan and Wu. As an application, we show that with boundary conditions corresponding to integer partitions
λ
, the six-vertex model is exactly solvable and equal to a Schur polynomial
s
λ
times a deformation of the Weyl denominator. This generalizes and gives a new proof of results of Tokuyama and Hamel and King.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-011-1345-3</identifier><identifier>CODEN: CMPHAY</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Classical and Quantum Gravitation ; Complex Systems ; Exact sciences and technology ; Mathematical and Computational Physics ; Mathematical methods in physics ; Mathematical Physics ; Other topics in mathematical methods in physics ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Theoretical</subject><ispartof>Communications in mathematical physics, 2011-12, Vol.308 (2), p.281-301</ispartof><rights>Springer-Verlag 2011</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c384t-366dc6aa361800dd26bef9a4eba007cc9c820b9e963e5605a8d9707e4f6ecf3c3</citedby><cites>FETCH-LOGICAL-c384t-366dc6aa361800dd26bef9a4eba007cc9c820b9e963e5605a8d9707e4f6ecf3c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,777,781,27905,27906</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24765431$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Brubaker, Ben</creatorcontrib><creatorcontrib>Bump, Daniel</creatorcontrib><creatorcontrib>Friedberg, Solomon</creatorcontrib><title>Schur Polynomials and The Yang-Baxter Equation</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map
from
to End
, where
V
is a two-dimensional vector space such that if
then
R
12
(
g
)
R
13
(
gh
)
R
23
(
h
) =
R
23
(
h
)
R
13
(
gh
)
R
12
(
g
). Here
R
i
j
denotes
R
applied to the
i
,
j
components of
. The image of this map consists of matrices whose nonzero coefficients
a
1
,
a
2
,
b
1
,
b
2
,
c
1
,
c
2
are the Boltzmann weights for the non-field-free six-vertex model, constrained to satisfy
a
1
a
2
+
b
1
b
2
−
c
1
c
2
= 0. This is the exact center of the disordered regime, and is contained within the free fermionic eight-vertex models of Fan and Wu. As an application, we show that with boundary conditions corresponding to integer partitions
λ
, the six-vertex model is exactly solvable and equal to a Schur polynomial
s
λ
times a deformation of the Weyl denominator. This generalizes and gives a new proof of results of Tokuyama and Hamel and King.</description><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Exact sciences and technology</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical methods in physics</subject><subject>Mathematical Physics</subject><subject>Other topics in mathematical methods in physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9j7tOwzAUhi0EEqXwAGxZGF2OL3HiEapSkCqBRBmYrBPHaVOlTrFbib49roIYmc7w385HyC2DCQMo7iMA50CBMcqEzKk4IyMmBaegmTonIwAGVCimLslVjBsA0FypEZm82_UhZG99d_T9tsUuZujrbLl22Sf6FX3E770L2ezrgPu299fkokked_N7x-TjabacPtPF6_xl-rCgVpRyn4ZUbRViGiwB6pqryjUapaswPWuttiWHSjuthMsV5FjWuoDCyUY52wgrxoQNvTb0MQbXmF1otxiOhoE5AZsB2CRgcwI2ImXuhswOo8WuCehtG_-CXBYql4IlHx98MUl-5YLZ9IfgE84_5T9UVGR5</recordid><startdate>20111201</startdate><enddate>20111201</enddate><creator>Brubaker, Ben</creator><creator>Bump, Daniel</creator><creator>Friedberg, Solomon</creator><general>Springer-Verlag</general><general>Springer</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20111201</creationdate><title>Schur Polynomials and The Yang-Baxter Equation</title><author>Brubaker, Ben ; Bump, Daniel ; Friedberg, Solomon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c384t-366dc6aa361800dd26bef9a4eba007cc9c820b9e963e5605a8d9707e4f6ecf3c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Exact sciences and technology</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical methods in physics</topic><topic>Mathematical Physics</topic><topic>Other topics in mathematical methods in physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Brubaker, Ben</creatorcontrib><creatorcontrib>Bump, Daniel</creatorcontrib><creatorcontrib>Friedberg, Solomon</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Brubaker, Ben</au><au>Bump, Daniel</au><au>Friedberg, Solomon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Schur Polynomials and The Yang-Baxter Equation</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2011-12-01</date><risdate>2011</risdate><volume>308</volume><issue>2</issue><spage>281</spage><epage>301</epage><pages>281-301</pages><issn>0010-3616</issn><eissn>1432-0916</eissn><coden>CMPHAY</coden><abstract>We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map
from
to End
, where
V
is a two-dimensional vector space such that if
then
R
12
(
g
)
R
13
(
gh
)
R
23
(
h
) =
R
23
(
h
)
R
13
(
gh
)
R
12
(
g
). Here
R
i
j
denotes
R
applied to the
i
,
j
components of
. The image of this map consists of matrices whose nonzero coefficients
a
1
,
a
2
,
b
1
,
b
2
,
c
1
,
c
2
are the Boltzmann weights for the non-field-free six-vertex model, constrained to satisfy
a
1
a
2
+
b
1
b
2
−
c
1
c
2
= 0. This is the exact center of the disordered regime, and is contained within the free fermionic eight-vertex models of Fan and Wu. As an application, we show that with boundary conditions corresponding to integer partitions
λ
, the six-vertex model is exactly solvable and equal to a Schur polynomial
s
λ
times a deformation of the Weyl denominator. This generalizes and gives a new proof of results of Tokuyama and Hamel and King.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s00220-011-1345-3</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
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| ispartof | Communications in mathematical physics, 2011-12, Vol.308 (2), p.281-301 |
| issn | 0010-3616 1432-0916 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s00220_011_1345_3 |
| source | Springer Link |
| subjects | Classical and Quantum Gravitation Complex Systems Exact sciences and technology Mathematical and Computational Physics Mathematical methods in physics Mathematical Physics Other topics in mathematical methods in physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical |
| title | Schur Polynomials and The Yang-Baxter Equation |
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