Geodesic
On multiple polynomials of Capelli type
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 1, pp. 5-25

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This paper deals with the class of Capelli polynomials in free associative algebra $F\{Z\}$ (where $F$ is an arbitrary field, $Z$ is a countable set) generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their $T$-ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established.
Mots-clés : matrix algebra, Capelli polynomial
Keywords: polynomial identity, free associative algebra, symmetric group, standard polynomial, $T$-ideal. 
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     author = {S. Y. Antonov and A. V. Antonova},
     title = {On multiple polynomials of {Capelli} type},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {5--25},
     publisher = {mathdoc},
     volume = {158},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2016_158_1_a0/}
}
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S. Y. Antonov; A. V. Antonova. On multiple polynomials of Capelli type. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 1, pp. 5-25. http://geodesic.mathdoc.fr/item/UZKU_2016_158_1_a0/