title: On an algebraic identity and formula Jacobi—Trudi
metadata.name: dc.contributor.author
metadata.value: Bekker, Boris M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ivanov, Oleg A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Merkurjev, Alexander S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-09-01T14:41:51Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-09-01T14:41:51Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-03
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/3831
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The first Jacobi—Trudi identity expresses Schur polynomials as certain determinants of matrices whose
  entries are complete homogeneous polynomials. The definition of Schur polynomials was given by Cauchy
  in 1815 as a quotient of certain determinants defined by an integer partition with at most n non-zero parts.
  Schur functions became very important because of their close relationship with the irreducible characters
  of both the symmetric groups and the general linear groups, and for their combinatorial applications. The
  Jacobi—Trudi identity was first stated by Jacobi in 1841 and proved by Nicola Trudi in 1864. Since then
  this identity and its numerous generalizations have been the focus of much attention due to the important
  role they play in various areas of mathematics including mathematical physics, representation theory, and
  algebraic geometry, and various proofs based on different ideas (in particular, a natural combinatorial
  proof using Young tableaux techniques) have been found. In our paper, we give a short and simple proof of the first Jacobi—Trudi identity and discuss its relationship with some other well-known polynomial
  identities. Refs 3.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при поддержке гранта RFBR N 14-01-00393 и гранта NSF DNS#1160206.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: a generalized Vandermonde determinant
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Schur polynomials
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On an algebraic identity and formula Jacobi—Trudi
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Bekker_Ivanov_et_al.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/3831/1/Bekker_Ivanov_et_al.pdf
resources.format: Adobe PDF
resources.size: 222,28 kB