{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:15:51Z","timestamp":1759335351583},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,4]]},"abstract":"<jats:p> In this paper we explicitly determine the Renner monoid \u211b and the cross section lattice \u039b of the symplectic algebraic monoid MSp<jats:sub>n<\/jats:sub> in terms of the Weyl group and the concept of admissible sets; it turns out that \u211b is a submonoid of \u211b<jats:sub>n<\/jats:sub>, the Renner monoid of the whole matrix monoid M<jats:sub>n<\/jats:sub>, and that \u039b is a sublattice of \u039b<jats:sub>n<\/jats:sub>, the cross section lattice of M<jats:sub>n<\/jats:sub>. <\/jats:p><jats:p> Cell decompositions in algebraic geometry are usually obtained by the method of [1]. We give a more direct definition of cells for MSp<jats:sub>n<\/jats:sub> in terms of the B \u00d7 B-orbits, where B is a Borel subgroup of the unit group G of MSp<jats:sub>n<\/jats:sub>. Each cell turns out to be the intersection of MSp<jats:sub>n<\/jats:sub> with a cell of M<jats:sub>n<\/jats:sub>. We also show how to obtain these cells using a carefully chosen one parameter subgroup. <\/jats:p>","DOI":"10.1142\/s0218196703001304","type":"journal-article","created":{"date-parts":[[2003,4,17]],"date-time":"2003-04-17T10:15:25Z","timestamp":1050574525000},"page":"111-132","source":"Crossref","is-referenced-by-count":16,"title":["THE RENNER MONOIDS AND CELL DECOMPOSITIONS OF THE SYMPLECTIC ALGEBRAIC MONOIDS"],"prefix":"10.1142","volume":"13","author":[{"given":"ZHENHENG","family":"LI","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada"}]},{"given":"LEX E.","family":"RENNER","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2307\/1970915"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0941-6"},{"key":"rf3","volume-title":"Finite Groups of Lie Type; Conjugacy Classes and Complex Characters","author":"Carter R.","year":"1985"},{"key":"rf4","doi-asserted-by":"crossref","unstructured":"C.\u00a0DeConcini and C.\u00a0Procesi, Complete symmetric varieties, Lecture Notes in Mathematics\u00a0996 (Springer, 1973)\u00a0pp. 1\u201344.","DOI":"10.1007\/BFb0063234"},{"key":"rf6","series-title":"LMS Monograph","volume-title":"An Introduction to Semigroup Theory","volume":"8","author":"Howie J. 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