On the Wronskian combinants of binary forms
Year: 2005
Type: preprint
Abstract: For generic binary forms $A_1,...,A_r$ of order $d$ we construct a class of combinants $C = \{\C_q: 0 \le q \le r, q \neq 1\}$, to be called the Wronskian combinants of the $A_i$. We show that the collection $C$ gives a projective imbedding of the Grassmannian $G(r,S_d)$, and as a corollary, any other combinant admits a formula as an iterated transvectant in the $C$. Our second main result characterizes those collections of binary forms which can arise as Wronskian combinants. These collections are the ones such that an associated algebraic differential equation has the maximal number of linearly independent polynomial solutions. Along the way we deduce some identities which connect Wronskians with transvectants.
Source: arXiv (Cornell University)
Institution: Laboratoire Analyse, Géométrie et Applications
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952937799