Naslov
A note on symmetric orderings

Autori
Škoda, Zoran

Izvornik
Acta mathematica Spalatensia (2757-1688) 1 (2020); 53-60

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Weyl algebra ; symmetric ordering

Sažetak
Let Aˆn be the completion by the degree of a differential operator of the n-th Weyl algebra with generators x1, . . . , xn, ∂1 , . . . , ∂n. Consider n elements X1, . . . , Xn in Aˆ n of the form Xi = xi + X∞ K=1 Xn l=1 Xn j=1 xlp K−1, l ij (∂)∂ j, where p K−1, l ij (∂) is a degree (K−1) homogeneous polynomial in ∂ 1 , . . . , ∂n, antisymmetric in subscripts i, j. Then for any natural k and any function i: {;1, . . . , k}; → {;1, . . . , n}; we prove X σ∈Σ(k) Xiσ(1) · · · Xiσ(k) . 1 = k! xi1 · · · xik , where Σ(k) is the symmetric group on k letters and . denotes the Fock action of the Aˆ n on the space of (commutative) polynomials.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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