Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems

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• 作者：A.N. Sergeev^a ; ^b ; ^{SergeevAN@info.sgu.ru" class="auth_mail" title="E-mail the corresponding author} ; A.P. Veselov^c ; ^d ; ^{A.P.Veselov@lboro.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Symmetric Lie superalgebras ; Quantum Calogero&ndash ; Moser systems
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：728-768
• 全文大小：657 K

文摘

The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero–Moser systems. In the special case of symmetric pair class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S000187081631180X&_mathId=si1.gif&_user=111111111&_pii=S000187081631180X&_rdoc=1&_issn=00018708&md5=7c6f697c02bfe16cbfe81ce3318bbe01" title="Click to view the MathML source">g=gl(n,2m),k=osp(n,2m)class="mathContainer hidden">class="mathCode">$\mathfrak{g}=\mathfrak{gl}(n,2m),\mathfrak{k}=\mathfrak{osp}(n,2m)$ we establish a natural bijection between projective covers of spherically typical irreducible class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S000187081631180X&_mathId=si2.gif&_user=111111111&_pii=S000187081631180X&_rdoc=1&_issn=00018708&md5=4483596200d3b0fcc5b119e5bf3cc62b" title="Click to view the MathML source">gclass="mathContainer hidden">class="mathCode">$\mathfrak{g}$-modules and the finite dimensional generalised eigenspaces of the algebra of Calogero–Moser integrals class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S000187081631180X&_mathId=si140.gif&_user=111111111&_pii=S000187081631180X&_rdoc=1&_issn=00018708&md5=96e7038e3e338276980c522c6db77703" title="Click to view the MathML source">D_n,mclass="mathContainer hidden">class="mathCode">${\mathfrak{D}}_{n,m}$ acting on the corresponding Laurent quasi-invariants class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S000187081631180X&_mathId=si4.gif&_user=111111111&_pii=S000187081631180X&_rdoc=1&_issn=00018708&md5=f5ffb2c8b82f983487d7e6f77ec25f05" title="Click to view the MathML source">A_n,mclass="mathContainer hidden">class="mathCode">${\mathfrak{A}}_{n,m}$.