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- W3081496564 abstract "The Kronecker coefficients, which are indexed by triples of partitions and describe how the tensor product of two irreducible representations of the symmetric group decomposes as a direct sum of such representations, were introduced by Francis Murnaghan in the 1930s. He notably noticed a remarkable behaviour of these coefficients: from any triple of partitions, one can construct a particular sequence of Kronecker coefficients which eventually stabilises.In order to generalise this property, John Stembridge introduced in 2014 a notion of stability for triples of partitions, as well as another notion -- of weakly stable triple -- about which he conjectured that it should be equivalent to the previous one. This conjecture was proven shortly after by Steven Sam and Andrew Snowden, with algebraic methods.In this thesis we especially give another proof -- this time geometric -- of this equivalence, using the classical expression of the Kronecker coefficients as dimensions of spaces of sections of line bundles on flag varieties. With these methods we can also be interested in more specific questions: since the stability which we discuss means that some sequences of coefficients stabilise, one can wonder at which point these sequences become constant.We then apply these techniques to other examples of branching coefficients, and are also interested in another problem: how can we produce stable triples of partitions? We thus generalise a result obtained independently by Laurent Manivel and Ernesto Vallejo on this subject" @default.
- W3081496564 created "2020-09-01" @default.
- W3081496564 creator A5029194185 @default.
- W3081496564 date "2017-11-24" @default.
- W3081496564 modified "2023-09-26" @default.
- W3081496564 title "Geometric Methods for stability-type results in representation theory" @default.
- W3081496564 hasPublicationYear "2017" @default.
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