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pro vyhledávání: '"Garge, Shripad"'
Autor:
Garge, Shripad, Sharma, Uday Bhaskar
Let $G$ be a group and $\alpha: G \times G \to G$ denote the commutator map. In the case of finite groups, Frobenius gave the formula to compute the cardinalities of the fibres $\alpha^{-1}(g)$ in terms of the character values $\chi(g)$ for irreducib
Externí odkaz:
http://arxiv.org/abs/2410.12282
For $1\le r\le n-1,$ let $G_{r,n}$ denote the Grassmannian parametrizing $r$-dimensional subspaces of $\mathbb{C}^{n}.$ Let $(r,n)=1.$ In this article we show that the GIT quotients of certain Richardson varieties in $G_{r,n}$ for the action of a max
Externí odkaz:
http://arxiv.org/abs/2306.15323
Autor:
Garge, Shripad M., Mitra, Oorna
Publikováno v:
Journal of Algebra, 606 (2022) 877-893
Let $F$ be a subfield of the algebraic closure of a finite field $\mathbb{F}_p$, $p \ne 2$, and let $R$ denote any ring such that $F[t] \subset R \subsetneq F(t)$. Let $G$ be a classical Chevalley group of adjoint type defined over $R$. We prove that
Externí odkaz:
http://arxiv.org/abs/2202.09757
Autor:
Garge, Shripad M., Pramanik, Arghya
Let $X$ be a smooth projective variety defined over a field $k$ of characteristic $0$ and let $\mathcal{L}$ be a nef line bundle defined over $k$. We prove that if $x\in X$ is a $k$-rational point then the Seshadri constant $\epsilon(X, \mathcal{L},
Externí odkaz:
http://arxiv.org/abs/2202.08074
Autor:
Garge, Shripad M.
We introduce the notion of commuting probability, $p(G)$, for an algebraic group $G$. This notion is inspired by the corresponding notions in finite groups and compact groups. The computation of $p(G)$ for reductive groups is readily done using the n
Externí odkaz:
http://arxiv.org/abs/2105.12550
Let $G$ be an algebraic group. For $d\geq 1$, we define the commuting probabilities $cp_d(G) = \frac{dim(\mathfrak C_d(G))}{dim(G^d)}$, where $\mathfrak C_d(G)$ is the variety of commuting $d$-tuples in $G$. We prove that for a reductive group $G$ wh
Externí odkaz:
http://arxiv.org/abs/2105.12930
Autor:
Garge, Shripad M., Singh, Anupam
Publikováno v:
Journal of Algebra, 554 (2020) 41-53
Let $k$ be a perfect field such that for every $n$ there are only finitely many field extensions, up to isomorphism, of $k$ of degree $n$. If $G$ is a reductive algebraic group defined over $k$, whose characteristic is very good for $G$, then we prov
Externí odkaz:
http://arxiv.org/abs/2001.06359
Autor:
Garge, Shripad M., Pramanik, Arghya
Publikováno v:
In Bulletin des sciences mathématiques February 2023 182
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Autor:
Garge, Shripad M., Singh, Anupam
Publikováno v:
In Journal of Algebra 15 July 2020 554:41-53