# The affine Lie algebra $\hat{\mathfrak{sl}_2}(\C)$ and a conditioned space-time Brownian motion

Abstract : We construct a sequence of Markov processes on the set of dominant weights of the Affine Lie algebra $\hat{\mathfrak{sl}_2}(\C)$ which involves tensor product of irreducible highest weight modules of $\hat{\mathfrak{sl}_2}(\C)$ and show that it converges towards a Doob's space-time harmonic transformation of a space-time Brownian motion.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00929811
Contributor : Manon Defosseux <>
Submitted on : Monday, March 17, 2014 - 12:30:26 PM
Last modification on : Tuesday, March 24, 2020 - 4:08:27 PM
Document(s) archivé(s) le : Tuesday, June 17, 2014 - 11:50:15 AM

### Files

BrownianAffinev3.pdf
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### Identifiers

• HAL Id : hal-00929811, version 3
• ARXIV : 1401.3115

### Citation

Manon Defosseux. The affine Lie algebra $\hat{\mathfrak{sl}_2}(\C)$ and a conditioned space-time Brownian motion. 2014. ⟨hal-00929811v3⟩

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