caa a22 4500 60616118X CHVBK 20210128100633.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10468-014-9495-6 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9495-6 Venkatesh R. Department of Mathematics, The Institute of Mathematical Sciences, 600113, Chennai, India aut Fusion Product Structure of Demazure Modules [Elektronische Daten] [R. Venkatesh] Let 𝔤 be a finite-dimensional complex simple Lie algebra. Given a non-negative integer ℓ, we define 𝓟 ℓ + $\mathcal {P}^{+}_{\ell }$ to be the set of dominant weights λ of 𝔤 such that ℓΛ0+λ is a dominant weight for the corresponding untwisted affine Kac-Moody algebra 𝔤 ̂ $\widehat {{\mathfrak {g}}}$ . For the current algebra 𝔤[t] associated to 𝔤, we show that the fusion product of an irreducible 𝔤-module V(λ) such that λ ∈ 𝓟 ℓ + $\lambda \in \mathcal {P}^{+}_{\ell }$ and a finite number of special family of 𝔤-stable Demazure modules of level ℓ (considered in Fourier and Littelmann, Nagoya Math. J. 182, 171-198 (2006), Adv. Math. 211(2), 566-593 2007) again turns out to be a Demazure module. This fact is closely related with several important conjectures. We use this result to construct the 𝔤[t]-module structure of the irreducible 𝔤 ̂ ${\widehat {\mathfrak {g}}}$ -module V(ℓ Λ0 + λ) as a semi-infinite fusion product of finite dimensional 𝔤[t]-modules as conjectured in Fourier and Littelmann, Adv. Math. 211(2), 566-593 (2007). As a second application we give further evidence to the conjecture on the generalization of Schur positivity (see Chari, Fourier and Sagaki 2013). Springer Science+Business Media Dordrecht, 2014 Fusion products nationallicence Demazure modules nationallicence Current algebras nationallicence Schur positivity nationallicence Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 307-321 1386-923X 18:2<307 2015 18 10468 https://doi.org/10.1007/s10468-014-9495-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9495-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Venkatesh R. Department of Mathematics, The Institute of Mathematical Sciences, 600113, Chennai, India aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 307-321 1386-923X 18:2<307 2015 18 10468