Naslov
Generators of relations for annihilating fields

Autori
Primc, Mirko

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Kac-Moody Lie Algebras and Related Topics, Contemporary Mathematics, Volume 343 / Sthanumoorthy, N. ; Kailash C. - Providence (RI) : American Mathematical Society (AMS), 2004, 229-241

Skup
Ramanujan International Symposium on Kac-Moody Lie Algebras and Applications

Mjesto i datum
Chennai, Indija, 28.01.2002. - 31.01.2002

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
affine Lie algebras; vertex operators

Sažetak
For an untwisted affine Kac-Moody Lie algebra $\tilde{;\mathfrak g};$, and a given positive integer level $k$, vertex operators $x(z)=\sum x(n)z^{;-n-1};$, $x\in\mathfrak g$, generate a vertex operator algebra $V$. For the maximal root $\theta$ and a root vector $x_\theta$ of the corresponding finite-dimensional $\mathfrak g$, the field $x_\theta(z)^{;k+1};$ generates all annihilating fields of level $k$ standard $\tilde{;\mathfrak g};$-modules. In this paper we study the kernel of the normal order product map $r(z)\otimes Y(v, z)\mapsto :r(z) Y(v, z):$ for $v\in V$ and $r(z)$ in the space of annihilating fields generated by the action of $\tfrac{;d};{;dz};$ and $\mathfrak g$ on $x_\theta(z)^{;k+1};$. We call the elements of this kernel the relations for annihilating fields, and the main result is that this kernel is generated, in certain sense, by the relation $x_\theta(z)\tfrac{;d};{;dz};(x_\theta(z)^{;k+1};)= (k+1)x_\theta(z)^{;k+1};\tfrac{;d};{;dz};x_\theta(z)$. This study is motivated by Lepowsky-Wilson's approach to combinatorial Rogers-Ramanujan type identities, and many ideas used here stem from a joint work with Arne Meurman.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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