Browsing by Author "Giri, Manabendra"

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    Crystallization of the quantized function algebras of SUq(n + 1)
    (Indian Statistical Institute, Delhi, 2025-05) Giri, Manabendra
    The $q$-deformation of a connected, simply connected Lie group $G$ is typically studied through two Hopf algebras associated with it: the quantized universal enveloping algebra $\mathcal{U}_q(\mathfrak{g})$ and the quantized function algebra $\mathcal{O}(G_q)$. If $G$ has a compact real form $K$, one can use the Cartan involution to give a $*$-structure on $\mathcal{O}(G_q)$. The QFA $\mathcal{O}(G_q)$ with this $*$ structure is denoted by $\mathcal{O}(K_q)$ and its $C^*$-completion by $C(K_q)$. Here we study the crystal limits of $\mathcal{O}(SU_q(n+1))$ and $C(SU_q(n+1))$ and classify all irreducible representations of the crystallized algebras. We also prove that the crystallized algebra carries a natural bialgebra structure.
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    Distinguishing attack on LDT
    (Indian Statistical Institute, Kolkata, 2018) Giri, Manabendra