NDLI: Asymptotics for the standard and the Capelli identities

Content Provider	Springer Nature Link
Author	Giambru, A. Zaicev, M.
Copyright Year	2003
Abstract	Let {c $_{ n }$(St $_{ k }$)} and {c $_{ n }$(C $_{ k }$)} be the sequences of codimensions of the T-ideals generated by the standard polynomial of degreek and by thek-th Capelli polynomial, respectively. We study the asymptotic behaviour of these two sequences over a fieldF of characteristic zero. For the standard polynomial, among other results, we show that the following asymptotic equalities hold: $$\begin{gathered} c_n \left( {St_{2k} } \right) \simeq c_n \left( {C_{k^2 + 1} } \right) \simeq c_n \left( {M_k \left( F \right)} \right), \enspace\enspace \\ c_n \left( {St_{2k + 1} } \right) \simeq c_n \left( {M_{k \times 2k} \left( F \right) \oplus M_{2k \times k} \left( F \right)} \right), \enspace\enspace \\ \end{gathered} $$ whereM $_{ k }$(F) is the algebra ofk×k matrices andM $_{ k×l }$(F) is the algebra of (K+l)×(k+l) matrices having the lastl rows and the lastk columns equal to zero. The precise asymptotics ofc $_{ n }$(M $_{ k }$(F)) are known and those ofM $_{ k×2k }$(F) andM $_{2k×k }$(F) can be easily deduced. For Capelli polynomials we show that also upper block triangular matrix algebras come into play.
Starting Page	125
Ending Page	145
Page Count	21
File Format	PDF
ISSN	00212172
Journal	Israel Journal of Mathematics
Volume Number	135
Issue Number	1
e-ISSN	15658511
Language	English
Publisher	Springer-Verlag
Publisher Date	2003-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Algebra Group Theory and Generalizations Analysis Applications of Mathematics Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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