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Showing 1 to 13 of 13 for “"Irreducible characters"”.
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Verification of the McKay-Alperin-Dade Conjecture for the covering groups of the Mathieu group M(22)
… Conjecture states that the number of complex irreducible characters with a given defect d in a p-block B of a finite group G can be expressed in terms of an alternating sum of the numbers of complex irreducible characters with related defects $d\sp\prime$ in related p-blocks $B\sp\prime$ of …
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Character sheaves on symmetric spaces
… the spherical functions (averages of the irreducible characters) of the associated symmetric space over a finite field. A crucial result about the filtration of character sheaves by cells enables us to compute the spherical functions explicitly in the cases GLn((Fq2)/GLn(]Fq) and …
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On Problems in the Representation Theory of Symmetric Groups
… $n$, we determine the maximum number of distinct irreducible constituents of degree coprime to $p$ of restrictions of irreducible characters of $\mathfrak{S}_n$ to $\mathfrak{S}_{n-1}$, and show that every value between 1 and this maximum is attained. These results can be stated …
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Radical <em>p</em>-chains in L<sub>3</sub>(2).
… finally verified, predicts the number of complex irreducible characters in various <em>p</em>-blocks of a finite group <em>G</em> as an alternating sum of the numbers of characters in related <em>p</em>-blocks of certain subgroups of <em>G</em>. The sub-groups involved are the normalizers of …
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Dade's Conjecture for the McLaughlin Simple Group
… a series of conjectures concerned with counting characters in the blocks of finite groups. Specifically, Dade's so-called Ordinary Conjecture asserts that if a finite group G has trivial p-core, and B is a p-block of G of positive defect, then the number k(B,d) of complex irreducible characters …
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On groups with few 𝑝′-character degrees
… that a finite group has exactly one non-linear irreducible character of degree greater than one if and only if the group is either an extraspecial 2-group or the group is isomorphic to a one-dimensional affine group over some field. An extension of Seitz’s theorem is Thompson’s celebrated …
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Dade's Conjecture for the McLaughlin Simple Group
… a series of conjectures concerned with counting characters in the blocks of finite groups. Specifically, Dade's so-called Ordinary Conjecture asserts that if a finite group G has trivial p-core and B is a p-block of G of positive defect, then the number $k(B,\ d)$ of complex irreducible …
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On projective representations on funite abelian group
… objective here is to determine the Inequivalent Irreducible projective representations of these groups which correspond to certain classes of factor sets. Let On'denote the direct product of n cyclic m groups C of order m.Then in [9] and [10] the a-regular classes have been determined; these …
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On projective representations on funite abelian group
… objective here is to determine the Inequivalent Irreducible projective representations of these groups which correspond to certain classes of factor sets. Let On'denote the direct product of n cyclic m groups C of order m.Then in [9] and [10] the a-regular classes have been determined; these …
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The Ordinary Weight conjecture and Dade's Projective Conjecture for p-blocks with an extra-special defect group
… \(d\), let \(k_d(B)\) denote the number of irreducible characters \(\chi\) in \(B\) which have \(\chi(1)_p=p^{a-d}\) and let \(k_d(b)\) be the corresponding number of \(b\). Various generalizations of Alperin's Weight Conjecture and McKay's Conjecture are due to Reinhard Knorr, Geoffrey R. …
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On Projective Characters of Rotation Sub- Group
… in [9] . In particular, formulae giving irreducible characters of these representations are explicitly determined in each case. Our object here is to apply the fore-going results to Rotation subgroups of Weyl groups of types Dg and D-, that o is, those groups which have Schur multiplier …
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On Projective Characters of Rotation Sub- Group
… in [9] . In particular, formulae giving irreducible characters of these representations are explicitly determined in each case. Our object here is to apply the fore-going results to Rotation subgroups of Weyl groups of types Dg and D-, that o is, those groups which have Schur multiplier …
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Semisimple filtrations of tilting modules for algebraic groups
… algorithm for calculating tilting characters from the irreducible characters. Applying Lusztig's character formula for the simple modules, we show that the algorithm agrees with Soergel's character formula for the regular indecomposable tilting modules for quantum groups at roots of …