Universality of High-Strength Tensors

A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given polynomial of the same degree in a bounded number of variables. Using entirely different techniques, we extend this theor...

Full description

Saved in:
Bibliographic Details
Published in:Vietnam journal of mathematics 2022, Vol.50 (2), p.557-580
Main Authors: Bik, Arthur, Danelon, Alessandro, Draisma, Jan, Eggermont, Rob H.
Format: Article
Language:English
Subjects:
High strength
Mathematics
Mathematics and Statistics
Original
Original Article
Polynomials
Tensors
Theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given polynomial of the same degree in a bounded number of variables. Using entirely different techniques, we extend this theorem to arbitrary polynomial functors. As a corollary of our work, we show that specialisation induces a quasi-order on elements in polynomial functors, and that among the elements with a dense orbit there are unique smallest and largest equivalence classes in this quasi-order.
ISSN:2305-221X
2305-2228
2305-2228
DOI:10.1007/s10013-021-00522-7