Geometries from Young diagrams
نویسندگان
چکیده
منابع مشابه
Geometries from Young Diagrams
Type IIB string theory on spacetimes that are asymptotically AdS5×S can be defined using four dimensional N = 4 super Yang-Mills theory. Six of the dimensions of the string theory are holographically reconstructed in the Yang-Mills theory. In this article we study how these dimensions and local physics in these dimensions emerge. We reorganize the dynamics of the 1 2 BPS sector of the field the...
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The well-known fact that there is always one more addable than removable box for a Young diagram is generalized to arbitrary hooks. As an application, this implies immediately a simple proof of a conjecture of Regev and Vershik 3] for which inductive proofs have recently been given by Regev and Zeilberger 4] and Janson 1].
متن کاملThe Permutation Group and Young Diagrams
The permutation, or symmetric, group, Sn is interesting at least partly because it contains subgroups isomorphic to all groups of order ≤ n. This result is known as “Cayley’s theorem”. It is also of great value in tensor analysis as the means to describe the tensor space in terms of symmetries under permutations of indicies. Here, we develop a diagrammatic approach to determining the irreducibl...
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The topics I want to treat have various sources: (1) the fundamental theorems of invariant theory of the classical groups, (2) the representation theory of classical groups, (3) the geometry of the Grassmann and flag varieties. The initial interest in these questions came for me from the solution given by Formanek and myself, [8], of Mumford's conjecture for the linear group, [25], obtained ind...
متن کاملProjecting onto Qubit Irreps of Young Diagrams
Let K be the diagonal subgroup of U(2)⊗n. For the onequbit state space H 1 = C{|0〉} ⊕C{|1〉}, we may view H 1 as a standard representation of U(2) and the n-qubit state space H n = (H 1)⊗n as the n-fold tensor product of standard representations. Representation theory then decomposes H n into irreducible subrepresentations of K parametrized by combinatorial objects known as Young diagrams. We ar...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2008
ISSN: 1029-8479
DOI: 10.1088/1126-6708/2008/11/061