On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups
In the group algebra of the symmetric group , we consider the subalgebra consisting of all functions invariant with respect to left and right shifts by elements of the Young subgroup . We discuss structure constants of the algebra and construct an algebra with continuous parameters extrapolating alg...
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| Veröffentlicht in: | Mathematical Notes 2023-10, Vol.114 (3-4), p.583-592 |
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| creator | Neretin, Yu. A. |
| description | In the group algebra of the symmetric group
, we consider the subalgebra
consisting of all functions invariant with respect to left and right shifts by elements of the Young subgroup
. We discuss structure constants of the algebra
and construct an algebra with continuous parameters
extrapolating algebras
, this can also be rewritten as an asymptotic algebra as
(for fixed
). We show that there is a natural map from the Lie algebra of the group of pure braids to
(and therefore this Lie algebra acts in spaces of multiplicities of the quasiregular representation of the group
in functions on
). |
| doi_str_mv | 10.1134/S0001434623090262 |
| format | Article |
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, we consider the subalgebra
consisting of all functions invariant with respect to left and right shifts by elements of the Young subgroup
. We discuss structure constants of the algebra
and construct an algebra with continuous parameters
extrapolating algebras
, this can also be rewritten as an asymptotic algebra as
(for fixed
). We show that there is a natural map from the Lie algebra of the group of pure braids to
(and therefore this Lie algebra acts in spaces of multiplicities of the quasiregular representation of the group
in functions on
).</description><identifier>ISSN: 0001-4346</identifier><identifier>ISSN: 1067-9073</identifier><identifier>EISSN: 1573-8876</identifier><identifier>DOI: 10.1134/S0001434623090262</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>14/34 ; 639/766/189 ; 639/766/530 ; 639/766/747 ; Algebra ; Group theory ; Lie groups ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Subgroups</subject><ispartof>Mathematical Notes, 2023-10, Vol.114 (3-4), p.583-592</ispartof><rights>Pleiades Publishing, Ltd. 2023</rights><rights>Pleiades Publishing, Ltd. 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c1832-7b341b30cc163d69335c30e63d79241a2c52b5e891d52069d66df4a5921a9d33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0001434623090262$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0001434623090262$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Neretin, Yu. A.</creatorcontrib><title>On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups</title><title>Mathematical Notes</title><addtitle>Math Notes</addtitle><description>In the group algebra of the symmetric group
, we consider the subalgebra
consisting of all functions invariant with respect to left and right shifts by elements of the Young subgroup
. We discuss structure constants of the algebra
and construct an algebra with continuous parameters
extrapolating algebras
, this can also be rewritten as an asymptotic algebra as
(for fixed
). We show that there is a natural map from the Lie algebra of the group of pure braids to
(and therefore this Lie algebra acts in spaces of multiplicities of the quasiregular representation of the group
in functions on
).</description><subject>14/34</subject><subject>639/766/189</subject><subject>639/766/530</subject><subject>639/766/747</subject><subject>Algebra</subject><subject>Group theory</subject><subject>Lie groups</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Subgroups</subject><issn>0001-4346</issn><issn>1067-9073</issn><issn>1573-8876</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1UE1LwzAYDqLgnP4AbwHP1bx5k7Q5jqlTGEzsLp5Km6Z1Y2tq0iL79-s2wYN4ej-eL3gIuQV2D4DiIWWMgUChODLNuOJnZAQyxihJYnVORgc4OuCX5CqE9XCBAjYib4uGTja1LXweqKvoo-uLjaVTF2x3fKS77dZ2fmXozLu-DfR71X3SdxtaazraOfrh-qamaV_UR_yaXFT5Jtibnzkmy-en5fQlmi9mr9PJPDKQII_iAgUUyIwBhaXSiNIgs8Meay4g50byQtpEQyk5U7pUqqxELjWHXJeIY3J3sm29--pt6LK1630zJGY8SQClUDEbWHBiGe9C8LbKWr_a5n6XAcsOvWV_ehs0_KQJA7eprf91_l-0B3YlbM8</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Neretin, Yu. A.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231001</creationdate><title>On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups</title><author>Neretin, Yu. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1832-7b341b30cc163d69335c30e63d79241a2c52b5e891d52069d66df4a5921a9d33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>14/34</topic><topic>639/766/189</topic><topic>639/766/530</topic><topic>639/766/747</topic><topic>Algebra</topic><topic>Group theory</topic><topic>Lie groups</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Subgroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Neretin, Yu. A.</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematical Notes</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Neretin, Yu. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups</atitle><jtitle>Mathematical Notes</jtitle><stitle>Math Notes</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>114</volume><issue>3-4</issue><spage>583</spage><epage>592</epage><pages>583-592</pages><issn>0001-4346</issn><issn>1067-9073</issn><eissn>1573-8876</eissn><abstract>In the group algebra of the symmetric group
, we consider the subalgebra
consisting of all functions invariant with respect to left and right shifts by elements of the Young subgroup
. We discuss structure constants of the algebra
and construct an algebra with continuous parameters
extrapolating algebras
, this can also be rewritten as an asymptotic algebra as
(for fixed
). We show that there is a natural map from the Lie algebra of the group of pure braids to
(and therefore this Lie algebra acts in spaces of multiplicities of the quasiregular representation of the group
in functions on
).</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0001434623090262</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0001-4346 |
| ispartof | Mathematical Notes, 2023-10, Vol.114 (3-4), p.583-592 |
| issn | 0001-4346 1067-9073 1573-8876 |
| language | eng |
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| source | SpringerNature Journals |
| subjects | 14/34 639/766/189 639/766/530 639/766/747 Algebra Group theory Lie groups Mathematical analysis Mathematics Mathematics and Statistics Subgroups |
| title | On Algebras of Double Cosets of Symmetric Groups with Respect to Young Subgroups |
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