@article{09903c713c064798b445d9d64ed8120f,

title = "Group actions and invariants in algebras of generic matrices",

abstract = "We show that the fixed elements for the natural GLm-action on the universal division algebra UD (m, n) of m generic n × n-matrices form a division subalgebra of degree n, assuming n ≥ 3 and 2 ≤ m ≤ n2 - 2. This allows us to describe the asymptotic behavior of the dimension of the space of SLm-invariant homogeneous central polynomials p (X1, ..., Xm) for n × n-matrices. Here the base field is assumed to be of characteristic zero.",

keywords = "Central polynomial, Concomitants, Gelfand-Kirillov dimension, Generic matrices, Geometric action, Group action, Invariants, PI-degree, Universal division algebra",

author = "Z. Reichstein and N. Vonessen",

note = "Funding Information: Keywords: Generic matrices; Universal division algebra; Central polynomial; PI-degree; Group action; Geometric action; Invariants; Concomitants; Gelfand–Kirillov dimension * Corresponding author. E-mail addresses: reichste@math.ubc.ca (Z. Reichstein), nikolaus.vonessen@umontana.edu (N. Vonessen). URLs: http://www.math.ubc.ca/~reichst (Z. Reichstein), http://www.math.umt.edu/vonessen (N. Vonessen). 1 Z. Reichstein was supported in part by an NSERC research grant. 2 N. Vonessen gratefully acknowledges the support of the University of Montana and the hospitality of the University of British Columbia during his sabbatical in 2002/2003, when part of this research was done.",

year = "2006",

month = oct,

doi = "10.1016/j.aam.2005.08.007",

language = "English",

volume = "37",

pages = "481--500",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Academic Press Inc.",

number = "4",

}