Group actions and invariants in algebras of generic matrices |
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| Authors: | Z Reichstein N Vonessen |
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| Institution: | aDepartment of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;bDepartment of Mathematical Sciences, University of Montana, Missoula, MT 59812-0864, USA |
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| 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 mn2−2. 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. |
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| Keywords: | Generic matrices Universal division algebra Central polynomial PI-degree Group action Geometric action Invariants Concomitants Gelfand– Kirillov dimension |
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