Let Uq(osp(1|2n)) be the quantized enveloping superalgebra corresponding to the Lie superalgebra osp(1|2n). In terms of semistandard Young tableaux satisfying some additional conditions, a realization of crystal graph...Let Uq(osp(1|2n)) be the quantized enveloping superalgebra corresponding to the Lie superalgebra osp(1|2n). In terms of semistandard Young tableaux satisfying some additional conditions, a realization of crystal graph of finite-dimensional irreducible modules of Uq(osp(1|2n)) is given. Also, the generalized LittlewoodRichardson rule for tensor product of crystal graphs is established.展开更多
Flagged skew tableaux are generalizationa of Young tableaux in which each row (column)has an upper and lower bound on the entries. It has been shown that they are enumerated byflagged skew Schur functions. By introduc...Flagged skew tableaux are generalizationa of Young tableaux in which each row (column)has an upper and lower bound on the entries. It has been shown that they are enumerated byflagged skew Schur functions. By introducing the dominance technique, we preeent an alternateproof for this conclusion directly.展开更多
The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux repre...The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an aspect of multipartite partitions. We discover, and show, that partitions can be expressed algebraically and can be “differentiated” and “integrated”. We show a complete set of bipartite and tripartite partitions, indicating equivalences for the root-pattern problem, for select pairs and triples. Tables enumerating the number of bipartite and tripartite partitions, for small pairs and triples are given in an appendix.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10671016 10771014)Beijing Natural Science Foundation (Grant No. 1062003)
文摘Let Uq(osp(1|2n)) be the quantized enveloping superalgebra corresponding to the Lie superalgebra osp(1|2n). In terms of semistandard Young tableaux satisfying some additional conditions, a realization of crystal graph of finite-dimensional irreducible modules of Uq(osp(1|2n)) is given. Also, the generalized LittlewoodRichardson rule for tensor product of crystal graphs is established.
文摘Flagged skew tableaux are generalizationa of Young tableaux in which each row (column)has an upper and lower bound on the entries. It has been shown that they are enumerated byflagged skew Schur functions. By introducing the dominance technique, we preeent an alternateproof for this conclusion directly.
文摘The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an aspect of multipartite partitions. We discover, and show, that partitions can be expressed algebraically and can be “differentiated” and “integrated”. We show a complete set of bipartite and tripartite partitions, indicating equivalences for the root-pattern problem, for select pairs and triples. Tables enumerating the number of bipartite and tripartite partitions, for small pairs and triples are given in an appendix.
