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UID:20260624T082120EDT-7829SPslA4@132.216.98.100
DTSTAMP:20260624T122120Z
DESCRIPTION:Title: Veronese sequence of analytic solutions of the $\mathbb{
 C}P^{2s}$ sigma model equations described via Krawtchouk polynomials.\n\nA
 bstract: The objective of this talk is to establish a new relationship bet
 ween the Veronese sequence of analytic solutions of the Euclidean $mathbb{
 C}P^{2s}$ sigma model in two dimensions and the orthogonal Krawtchouk poly
 nomials. We show that such solutions of the $mathbb{C}P^{2s}$ model\, defi
 ned on the Riemann sphere and having a finite action\, can be explicitly p
 arametrised in terms of these polynomials. We apply the obtained results t
 o the analysis of surfaces associated with $mathbb{C}P^{2s}$ sigma models\
 , defined using the generalized Weierstrass formula for immersion. We show
  that these surfaces are non-intersecting spheres immersed in the $mathfra
 k{su}(2s+1)$ Lie algebra\, and express several other geometrical character
 istics in terms of the Krawtchouk polynomials. Finally\, a new connection 
 between the $mathfrak{su}(2)$ spin-s representation and the $mathbb{C}P^{2
 s}$ model is explored in detail. It is shown that for any given holomorphi
 c vector function in $mathbb{C}^{2s+1}$ written as a Veronese sequence\, i
 t is possible to derive a sequence of analytic solutions of the $mathbb{C}
 P^{2s}$ model through algebraic recurrence relations which turn out to be 
 simpler than the analytic relations known in the literature. Joint work wi
 th Nicolas Crampé.\n
DTSTART:20191105T203000Z
DTEND:20191105T213000Z
LOCATION:Room 4336
SUMMARY:Michel Grundland\, UQTR et CRM
URL:/mathstat/channels/event/michel-grundland-uqtr-et-
 crm-302174
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