Geodesic
ON THE LINEAR COMBINANTS OF A BINARY PENCIL
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 481-498

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DOI

Let A, B denote binary forms of order d, and let 2r−1 = (A, B)2r−1 be the sequence of their linear combinants for . It is known that 1, 3 together determine the pencil {A + λ B}λ∈P1 and hence indirectly the higher combinants 2r−1. In this paper we exhibit explicit formulae for all r ≥ 3, which allow us to recover 2r−1 from the knowledge of 1 and 3. The calculations make use of the symbolic method in classical invariant theory, as well as the quantum theory of angular momentum. Our theorem pertains to the plethysm representation ∧2Sd 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.
DOI : 10.1017/S0017089509005126
Mots-clés : 13A50, 22E70 
ABDESSELAM, ABDELMALEK; CHIPALKATTI, JAYDEEP. ON THE LINEAR COMBINANTS OF A BINARY PENCIL. Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 481-498. doi: 10.1017/S0017089509005126
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     title = {ON {THE} {LINEAR} {COMBINANTS} {OF} {A} {BINARY} {PENCIL}},
     journal = {Glasgow mathematical journal},
     pages = {481--498},
     year = {2009},
     volume = {51},
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     doi = {10.1017/S0017089509005126},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509005126/}
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