Radha Kessar
YOU?
Author Swipe
View article: Jordan correspondence and block distribution of characters
Jordan correspondence and block distribution of characters Open
We complete the determination of the ‐block distribution of characters for quasi‐simple exceptional groups of Lie type up to some minor ambiguities relating to non‐uniqueness of Jordan decomposition. For this, we first determine the ‐block…
View article: Weight conjectures for Parker--Semeraro fusion systems
Weight conjectures for Parker--Semeraro fusion systems Open
We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the prin…
View article: Weights for compact connected Lie groups
Weights for compact connected Lie groups Open
Let $$\ell $$ be a prime. If $$\textbf{G}$$ is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from $$\ell $$ , and $$\ell $$ is a good prime for $$\textbf{G}$$ , we show that t…
View article: Jordan correspondence and block distribution of characters
Jordan correspondence and block distribution of characters Open
We complete the determination of the $\ell$-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the …
View article: PEM series 2 volume 66 issue 3 Cover and Front matter
PEM series 2 volume 66 issue 3 Cover and Front matter Open
View article: Hochschild cohomology of symmetric groups and generating functions, II
Hochschild cohomology of symmetric groups and generating functions, II Open
We relate the generating functions of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups with those of blocks of the symmetric groups. We show that the first Hochschild cohomology of a positive defect b…
View article: PEM series 2 volume 66 issue 2 Cover and Front matter
PEM series 2 volume 66 issue 2 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
View article: The principal block of a ℤℓ-spets and Yokonuma type algebras
The principal block of a ℤℓ-spets and Yokonuma type algebras Open
We formulate conjectures concerning the dimension of the principal block of a Z ℓ -spets (as defined in our earlier paper), motivated by analogous statements for finite groups.We show that these conjectures hold in certain situations.For t…
View article: The principal block of a ℤℓ-spets and Yokonuma type algebras
The principal block of a ℤℓ-spets and Yokonuma type algebras Open
We formulate conjectures concerning the dimension of the principal block of a ޚ ℓ -spets (as defined in our earlier paper), motivated by analogous statements for finite groups.We show that these conjectures hold in certain situations.For…
View article: Weights for compact connected Lie groups
Weights for compact connected Lie groups Open
Let $\ell$ be a prime. If ${\mathbf G} $ is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from $\ell$, and $\ell$ is a good prime for ${\mathbf G}$, we show that the number of weights o…
View article: PEM series 2 volume 66 issue 1 Cover and Front matter
PEM series 2 volume 66 issue 1 Cover and Front matter Open
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
View article: Hochschild cohomology of symmetric groups and generating functions,II
Hochschild cohomology of symmetric groups and generating functions,II Open
We relate the generating functions of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups with those of blocks of the symmetric groups. We show that the first Hochschild cohomology of a positive defect b…
Structure of blocks with normal defect and abelian inertial quotient Open
View article: Hochschild cohomology of symmetric groups in low degrees
Hochschild cohomology of symmetric groups in low degrees Open
We compute the dimensions of the Hochschild cohomology of symmetric groups over prime fields in low degrees. This involves us in studying some partition identities and generating functions of the dimensions in any fixed degree of the Hochs…
View article: Structure of blocks with normal defect and abelian $p'$ inertial quotient
Structure of blocks with normal defect and abelian $p'$ inertial quotient Open
Let $k$ be an algebraically closed field of prime characteristic $p$. Let $kGe$ be a block of a group algebra of a finite group $G$, with normal defect group $P$ and abelian $p'$ inertial quotient $L$. Then we show that $kGe$ is a matrix a…
View article: On the BV structure of the Hochschild cohomology of finite group algebras
On the BV structure of the Hochschild cohomology of finite group algebras Open
We give a simple algebraic recipe for calculating the components of the BV operator $Δ$ on the Hochschild cohomology of a finite group algebra with respect to the centraliser decomposition. We use this to investigate the properties of $Δ$ …
View article: A block theoretic proof of Thompson’s $$A\times B$$-lemma
A block theoretic proof of Thompson’s $$A\times B$$-lemma Open
View article: The principal block of a $\mathbb{Z}_\ell$-spets and Yokonuma type algebras
The principal block of a $\mathbb{Z}_\ell$-spets and Yokonuma type algebras Open
We formulate conjectures concerning the dimension of the principal block of a ${\mathbb Z}_\ell$-spets (as defined in our earlier paper), motivated by analogous statements for finite groups. We show that these conjectures hold in certain s…
View article: Weight conjectures for $\ell$-compact groups and spetses
Weight conjectures for $\ell$-compact groups and spetses Open
Fundamental conjectures in modular representation theory of finite groups, more precisely, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture, can be expressed in terms of fusion systems. We use fusion systems to connect…
View article: BLOCKS WITH NORMAL ABELIAN DEFECT AND ABELIAN p′ INERTIAL QUOTIENT
BLOCKS WITH NORMAL ABELIAN DEFECT AND ABELIAN p′ INERTIAL QUOTIENT Open
Let $k$ be an algebraically closed field of characteristic $p$, and let ${\mathcal{O}}$ be either $k$ or its ring of Witt vectors $W(k)$. Let $G$ be a finite group and $B$ a block of ${\mathcal{O}} G$ with normal abelian defect group and a…
View article: Rationality of blocks of quasi-simple finite groups
Rationality of blocks of quasi-simple finite groups Open
Let be a prime number. We show that the Morita Frobenius number of an -block of a quasi-simple finite group is at most and that the strong Frobenius number is at most , where denotes a defect group of the block. We deduce that a basic a…
View article: Weight conjectures for fusion systems
Weight conjectures for fusion systems Open
View article: On Picard groups of blocks of finite groups
On Picard groups of blocks of finite groups Open
View article: On Perverse Equivalences and Rationality
On Perverse Equivalences and Rationality Open
We show that perverse equivalences between module categories of finite-dimensional algebras preserve rationality. As an application, we give a connection between some famous conjectures from the modular representation theory of finite grou…
View article: Dade’s ordinary conjecture implies the Alperin–McKay conjecture
Dade’s ordinary conjecture implies the Alperin–McKay conjecture Open
View article: Local-global conjectures and blocks of simple groups
Local-global conjectures and blocks of simple groups Open
We give an expanded treatment of our lecture series at the 2017 Groups St Andrews conference in Birmingham on local-global conjectures and the block theory of finite reductive groups.
View article: Local Representation Theory and Simple Groups
Local Representation Theory and Simple Groups Open
The book contains extended versions of seven short lecture courses given during a semester programme on Local Representation Theory and Simple Groups, held at the Centre Interfacultaire Bernoulli of the EPF Lausanne. These courses focused …
View article: Descent of Equivalences and Character Bijections
Descent of Equivalences and Character Bijections Open
View article: On blocks of defect two and one simple module, and Lie algebra structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>H</mml:mi><mml:mspace width="-0.20em"/><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>
On blocks of defect two and one simple module, and Lie algebra structure of Open
View article: On blocks of defect two and one simple module, and Lie algebra structure of $HH^1$
On blocks of defect two and one simple module, and Lie algebra structure of $HH^1$ Open
Let $k$ be a field of odd prime characteristic $p$. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over $k$. As a consequence, we prove that if $B$ is a defect $2$-blo…