Permutation enumeration symmetric functions, and unimodality. Unimodal sequences arising from lie algebras mit math. On sequences associated to the invariant theory of rank. Some unimodal polynomials arising from lie algebras we begin this section with some technical definitions concerning lie algebras and representations 7,8. The dimension of the lie algebra v is just its dimension as a vector space over c. Stanley, unimodal sequences arising from lie algebras, alfred young day proceedings t. You will be notified whenever a record that you have chosen has been cited.
The koh terms and classes of unimodal nmodular diagrams. Unimodality via kronecker products journal of algebraic. Louisiana state university lsu digital commons lsu doctoral dissertations graduate school 582020 combinatorial and asymptotic statistical properties of partitions and unimodal s. On sequences associated to the invariant theory of lie algebras 3 given the sequence a with nth term an, the binomial transform of a is the sequence, denoted ba, whose nth term is n. It is wellknown how the representation theory of the lie algebra sl2. Logconcave and unimodal sequences arise often in combinatorics. This alert has been successfully added and will be sent to. Kruyswidk,on the set of divisors of a number, nieuw arch. Lie algebras arising from nichols algebras of diagonal type 3 table 1.
Stanley, unimodal sequences arising from lie algebras, combinatorics. Unimodal polynomials associated with lie algebras and. Combinatorial representation theory of lie algebras. Similarly, a sequence of positive integers uia is unimodal if 2 is. Combinatorics, representation theory and statistical methods in groups, lecture notes in pure and appl. The bruhat posets arising from weyl groups which are lattices are classified. Some unimodal polynomials arising from lie algebras we begin this section with some technical definitions concerning lie algebras and representa tions 7,8. Unimodal polynomials arise often in combinatorics, geometry, and algebra and have been the subject of considerable research in recent years. Combinatorics, representation theory and statistical methods in groups, lecture notes in. Unimodal sequences arising from lie algebras, combinatorics, representation theory and statistical methods in groups, 1276. Similar results unimodality, sperner property were derived by richard in. Lie algebras arising from nichols algebras of arxiv. Unimodal polynomials arise often in combinatorics, geometry, and algebra.
Lecture notes on lie groups and lie algebras contents 0. Unimodal sequence generating functions arising from. On the unimodality of some partition polynomials core. G contains an ldimensional diagonalisable abelian subalgebra h, the socalled cartan subalgebra. Stanley, r unimodal sequences arising from lie algebras. We wish to discuss a connection between combinatorial theory and the. Stanley, unimodal sequences arising from lie algebras, alfred young day. Our focus in this survey is on sequences arising as ehrhart h. Browse other questions tagged linear algebra grouptheory lie groups lie algebras or ask your own question. In combinatorics, representation theory and statistical methods in groups, 57. Ams, american mathematical society, the tricolored ams logo, and advancing research, creating connections, are trademarks and services marks of the american mathematical society and registered in the u. It is wellknown how the representation theory of the lie algebra sl 2.
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