
Recent Posts
Archives
 May 2020
 April 2020
 March 2020
 June 2018
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Tag Archives: partitions
Polynomials and Representations XXXVII
Notations and Recollections For a partition , one takes its Young diagram comprising of boxes. A filling is given by a function for some positive integer m. When m=d, we will require the filling to be bijective, i.e. T contains {1,…,d} and each element occurs exactly … Continue reading
Polynomials and Representations XXVII
From the previous article, we have columns j < j’ in the column tabloid U, and given a set A (resp. B) of boxes in column j (resp. j’), we get: where is the column tabloid obtained by swapping contents of A with B while preserving the order. … Continue reading
Polynomials and Representations XXVI
Let us fix a filling of shape and consider the surjective homomorphism of modules given by rightmultiplying by Specifically, we will describe its kernel, which will have interesting consequences when we examine representations of later. Row and Column Tabloids By the … Continue reading
Posted in Uncategorized
Tagged partitions, representation theory, symmetric group, young symmetrizer, young tableaux
Leave a comment
Polynomials and Representations XXV
Properties of the Young Symmetrizer Recall that for a filling , we have the subgroup of elements which take an element of the ith row (resp. column) of T to the ith row (resp. column) of T. Then: where is the Young symmetrizer. … Continue reading
Posted in Uncategorized
Tagged partitions, representation theory, symmetric group, young symmetrizer, young tableaux
Leave a comment
Polynomials and Representations XXIII
PowerSum Polynomials We will describe how the character table of is related to the expansion of the powersum symmetric polynomials in terms of monomials. Recall: where exactly since is not defined. Now each irrep of is of the form for some … Continue reading
Posted in Uncategorized
Tagged character theory, combinatorics, partitions, symmetric group, symmetric polynomials
Leave a comment
Polynomials and Representations XIV
In this article, we describe a way of removing the internal squares of a skew SSYT to turn it into an SSYT. Definition. First write the skew diagram as ; we define an inside corner to be a square in such that there is … Continue reading
Posted in Uncategorized
Tagged partitions, skew diagrams, sliding algorithm, young tableaux
Leave a comment
Polynomials and Representations XI
Here, we will give a different interpretation of the Schur polynomial, however this definition only makes sense in the ring For a given vector of nonnegative integers, define the following determinant, a polynomial in : For the case where , we … Continue reading
Posted in Uncategorized
Tagged determinants, partitions, pieri's formula, schur polynomials, young tableaux
Leave a comment