# 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.
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Preprints, Working Papers, ...
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Cited literature [9 references]

https://hal.archives-ouvertes.fr/hal-00929811
Contributor : Manon Defosseux <>
Submitted on : Monday, June 2, 2014 - 12:26:34 PM
Last modification on : Friday, September 20, 2019 - 4:34:03 PM
Long-term archiving on: Tuesday, September 2, 2014 - 12:10:12 PM

### Files

BrownianAffinev4.pdf
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### Identifiers

• HAL Id : hal-00929811, version 4
• ARXIV : 1401.3115

### Citation

Manon Defosseux. The affine Lie algebra $\hat{\mathfrak{sl}_2}(\C)$ and a conditioned space-time Brownian motion. 2014. ⟨hal-00929811v4⟩

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