2008/02/21 by Abdelmalek Abdesselam, Abdesselam, Abdelmalek, Jaydeep Chipalkatti +1 · 1 citation
Computer Science · Engineering · Mathematics · #13A50 #22E70 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Representation Theory (math.RT) #graph theory and CDMA systems #math.AG #math.RT #msc:13A50 #msc:22E70
paper · pdf · doi:10.48550/arxiv.0802.3149
LaTeX, 18 pages
arxiv created 2008/02/21 · openalex publication_date 2008/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A,B denote binary forms of order d, and let C2r-1 = (A,B)2r-1 be the sequence of their linear combinants for r between 1 and (d+1)/2. It is known that C1 and C3 together determine the pencil generated by A and B, and hence indirectly the higher C2r-1. In this paper we exhibit explicit formulae for all r>2, which allow us to recover C2r-1 from the knowledge of C1 and C3. The calculations make use of the symbolic method of classical invariant theory, as well as the quantum theory of angular momentum. Our theorem pertains to the second exterior power representation of Sd, for the group SL2. We give an example for the group SL3 to show that such a result may hold for other categories of representations.