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ndltd-NEU--neu-m046qg40b
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ndltd-NEU--neu-m046qg40b2021-06-02T05:10:09ZOn categories O of quiver varieties overlying the bouquet graphsWe study representation theory of quantizations of Nakajima quiver varieties associated to bouquet quivers. We show that there are no finite dimensional representations of the quantizations $\overline{\mathcal{A}}_{\lambda}(n, \ell)$ if both $\mbox{dim}~V=n$ and the number of loops $\ell$ are greater than $1$. We show that when $n\leq 3$ there is a Hamiltonian torus action with finitely many fixed points, provide the dimensions of Hom-spaces between standard objects in category $\mathcal{O}$ and compute the multiplicities of simples in standards for $n=2$ in case of one-dimensional framing and generic one-parameter subgroups. We establish the abelian localization theorem and find the values of parameters, for which the quantizations have infinite homological dimension.--Author's abstracthttp://hdl.handle.net/2047/D20382841
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NDLTD
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NDLTD
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| description |
We study representation theory of quantizations of Nakajima quiver varieties
associated to bouquet quivers. We show that there are no finite dimensional representations
of the quantizations $\overline{\mathcal{A}}_{\lambda}(n, \ell)$ if both $\mbox{dim}~V=n$
and the number of loops $\ell$ are greater than $1$. We show that when $n\leq 3$ there is a
Hamiltonian torus action with finitely many fixed points, provide the dimensions of
Hom-spaces between standard objects in category $\mathcal{O}$ and compute the multiplicities
of simples in standards for $n=2$ in case of one-dimensional framing and generic
one-parameter subgroups. We establish the abelian localization theorem and find the values
of parameters, for which the quantizations have infinite homological
dimension.--Author's abstract
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On categories O of quiver varieties overlying the bouquet graphs
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| spellingShingle |
On categories O of quiver varieties overlying the bouquet graphs
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| title_short |
On categories O of quiver varieties overlying the bouquet graphs
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| title_full |
On categories O of quiver varieties overlying the bouquet graphs
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| title_fullStr |
On categories O of quiver varieties overlying the bouquet graphs
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| title_full_unstemmed |
On categories O of quiver varieties overlying the bouquet graphs
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| title_sort |
on categories o of quiver varieties overlying the bouquet graphs
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| url |
http://hdl.handle.net/2047/D20382841
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1719408415932940288
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