A Note on Categorification and Spherical Harmonics
Using Khovanov’s categorification of the Weyl algebra, we investigate categorical structures arising from spherical harmonics. We categorify the s l ( 2 , ℂ ) -action on the polynomial ring in n variables, and use this to categorify certain simple Verma modules. On the way we also categorify the sta...
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| Veröffentlicht in: | Algebras and representation theory 2020-08, Vol.23 (4), p.1285-1295 |
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| container_issue | 4 |
| container_start_page | 1285 |
| container_title | Algebras and representation theory |
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| creator | Arunasalam, Suntharan Ciappara, Joshua Nguyen, Diana M. H. Tan, Suo Jun Yacobi, Oded |
| description | Using Khovanov’s categorification of the Weyl algebra, we investigate categorical structures arising from spherical harmonics. We categorify the
s
l
(
2
,
ℂ
)
-action on the polynomial ring in
n
variables, and use this to categorify certain simple Verma modules. On the way we also categorify the standard action of matrix units
E
ij
∈
g
l
(
n
,
ℂ
)
on the polynomial ring. |
| doi_str_mv | 10.1007/s10468-019-09886-4 |
| format | Article |
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s
l
(
2
,
ℂ
)
-action on the polynomial ring in
n
variables, and use this to categorify certain simple Verma modules. On the way we also categorify the standard action of matrix units
E
ij
∈
g
l
(
n
,
ℂ
)
on the polynomial ring.</description><identifier>ISSN: 1386-923X</identifier><identifier>EISSN: 1572-9079</identifier><identifier>DOI: 10.1007/s10468-019-09886-4</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Associative Rings and Algebras ; Commutative Rings and Algebras ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Non-associative Rings and Algebras ; Polynomials ; Rings (mathematics) ; Spherical harmonics</subject><ispartof>Algebras and representation theory, 2020-08, Vol.23 (4), p.1285-1295</ispartof><rights>Springer Nature B.V. 2019</rights><rights>Springer Nature B.V. 2019.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-ed91d8b53724a3e8523de2f4362ad49bff7a50f2f199da13adbe6251a066158a3</citedby><cites>FETCH-LOGICAL-c319t-ed91d8b53724a3e8523de2f4362ad49bff7a50f2f199da13adbe6251a066158a3</cites><orcidid>0000-0002-8330-7424</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10468-019-09886-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10468-019-09886-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Arunasalam, Suntharan</creatorcontrib><creatorcontrib>Ciappara, Joshua</creatorcontrib><creatorcontrib>Nguyen, Diana M. H.</creatorcontrib><creatorcontrib>Tan, Suo Jun</creatorcontrib><creatorcontrib>Yacobi, Oded</creatorcontrib><title>A Note on Categorification and Spherical Harmonics</title><title>Algebras and representation theory</title><addtitle>Algebr Represent Theor</addtitle><description>Using Khovanov’s categorification of the Weyl algebra, we investigate categorical structures arising from spherical harmonics. We categorify the
s
l
(
2
,
ℂ
)
-action on the polynomial ring in
n
variables, and use this to categorify certain simple Verma modules. On the way we also categorify the standard action of matrix units
E
ij
∈
g
l
(
n
,
ℂ
)
on the polynomial ring.</description><subject>Associative Rings and Algebras</subject><subject>Commutative Rings and Algebras</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Non-associative Rings and Algebras</subject><subject>Polynomials</subject><subject>Rings (mathematics)</subject><subject>Spherical harmonics</subject><issn>1386-923X</issn><issn>1572-9079</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEUxIMoWKtfwNOC52jy8meTYylqhaIHFbyF7CapW9rNmmwPfnujK3jz9IZhZh78ELqk5JoSUt9kSrhUmFCNiVZKYn6EZlTUgDWp9XHRrJga2NspOst5SwjRUtEZgkX1GEdfxb5a2tFvYupC19qxK4btXfU8vPtUjF21smkf-67N5-gk2F32F793jl7vbl-WK7x-un9YLta4ZVSP2DtNnWoEq4Fb5pUA5jwEziRYx3UTQm0FCRCo1s5SZl3jJQhqiZRUKMvm6GraHVL8OPg8mm08pL68NMBBSACoVUnBlGpTzDn5YIbU7W36NJSYbzZmYmMKG_PDxvBSYlMpl3C_8elv-p_WF74vZcg</recordid><startdate>20200801</startdate><enddate>20200801</enddate><creator>Arunasalam, Suntharan</creator><creator>Ciappara, Joshua</creator><creator>Nguyen, Diana M. H.</creator><creator>Tan, Suo Jun</creator><creator>Yacobi, Oded</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-8330-7424</orcidid></search><sort><creationdate>20200801</creationdate><title>A Note on Categorification and Spherical Harmonics</title><author>Arunasalam, Suntharan ; Ciappara, Joshua ; Nguyen, Diana M. H. ; Tan, Suo Jun ; Yacobi, Oded</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-ed91d8b53724a3e8523de2f4362ad49bff7a50f2f199da13adbe6251a066158a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Associative Rings and Algebras</topic><topic>Commutative Rings and Algebras</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Non-associative Rings and Algebras</topic><topic>Polynomials</topic><topic>Rings (mathematics)</topic><topic>Spherical harmonics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Arunasalam, Suntharan</creatorcontrib><creatorcontrib>Ciappara, Joshua</creatorcontrib><creatorcontrib>Nguyen, Diana M. H.</creatorcontrib><creatorcontrib>Tan, Suo Jun</creatorcontrib><creatorcontrib>Yacobi, Oded</creatorcontrib><collection>CrossRef</collection><jtitle>Algebras and representation theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Arunasalam, Suntharan</au><au>Ciappara, Joshua</au><au>Nguyen, Diana M. H.</au><au>Tan, Suo Jun</au><au>Yacobi, Oded</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Note on Categorification and Spherical Harmonics</atitle><jtitle>Algebras and representation theory</jtitle><stitle>Algebr Represent Theor</stitle><date>2020-08-01</date><risdate>2020</risdate><volume>23</volume><issue>4</issue><spage>1285</spage><epage>1295</epage><pages>1285-1295</pages><issn>1386-923X</issn><eissn>1572-9079</eissn><abstract>Using Khovanov’s categorification of the Weyl algebra, we investigate categorical structures arising from spherical harmonics. We categorify the
s
l
(
2
,
ℂ
)
-action on the polynomial ring in
n
variables, and use this to categorify certain simple Verma modules. On the way we also categorify the standard action of matrix units
E
ij
∈
g
l
(
n
,
ℂ
)
on the polynomial ring.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10468-019-09886-4</doi><tpages>11</tpages><orcidid>https://orcid.org/0000-0002-8330-7424</orcidid></addata></record> |
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| identifier | ISSN: 1386-923X |
| ispartof | Algebras and representation theory, 2020-08, Vol.23 (4), p.1285-1295 |
| issn | 1386-923X 1572-9079 |
| language | eng |
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| source | SpringerNature Journals |
| subjects | Associative Rings and Algebras Commutative Rings and Algebras Mathematical analysis Mathematics Mathematics and Statistics Non-associative Rings and Algebras Polynomials Rings (mathematics) Spherical harmonics |
| title | A Note on Categorification and Spherical Harmonics |
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