Department of Mathematics and Statistics

Bar-Ilan University

Ramat Gan, Israel 52900

Tel. 972-3-5318767

Fax 972-3-6161752

- Curriculum Vitae
- List of Publications
- Database of groups of order up to 100
- The p'-subgroups of GL2_p for p = 3, 5, 7, 11, 13.
- Database of blocks of cyclic defect for primes 5, 7 11, 13, 17, and 19.
- Database of blocks of noncyclic abelian defect for primes 3 , 5 and 7
- Database of spin blocks of the symmetric and alternating groups for primes 3 and 5
- Database of blocks of sporadic simple groups for invariants by groups, with defect 0
- Link to Atlas of Finite Group Representations
- Link to GAP4 Manual
- Atlas of Lie Groups and Representations
- Sage homepage
- Sage notebook interface
### Recent preprints: TeX files.

- (with Hussam Arisha) "Maximal strings in the crystal graph of spin representations of the symmetric and alternating groups"(pdf) Combinatorics of the crystal graph.dvi Fig.1 Fig.2
- Explicit tilting complexes for the Broue conjecture on 3-blocks(with A. Bar-Ilan, Tz. Berrebi, G. Chereshnya, R. Leabovich, M. Cohen). Explicit tilting complexes are calculated for a number of 3-blocks and the databases of such blocks given above are described, to appear in the Proceedings of Groups St. Andrews 2005.pdf file.
*Crossover Morita equivalences for blocks of the covering groups of the symmetric and alternating groups*(with R. Kessar). In cases where the Scopes involution reverses parity, p-permutation modules are used to demonstrate Morita equivalences between blocks with corresponding cores, preprint.*The Broue conjecture for the faithful blocks of 4.M22*(with J. Mueller). Construction of a tilting complex for these blocks, using Puig construction of the stable equivalence for Frobenius actions, preprint.*Two-sided combinatorial tilting complexes*(with J. Rickard). Construction of two-sided tilting complex in cyclic defect case. Relationship between Green correspondence and folding of the tilting complex, preprint.*Lifting McKay graphs and relations to prime extensions*, with Mohammed Hasan Ali.

Studies the relationship between the McKay graph of a subgroup of finite index and an irreducible character and the corresponding McKay graph of an extension, to appear in the Rocky Mountain J.,2006.ps file,tex file*Deformations, Tiltings, and Decomposition Matrices*(.ps file)Decomposition matrices for general separable deformations and relationship to tilting complexes. Mixed "folding" for elementary tilting complexes as used by Okuyama. To appear in Proceedings of ICRA X, (2005).*Two-dimensional pattern matching with rotation*

(with A. Amir, A. Butman, M. Crochemore, G.M. Landau). Two methods for matching patterns appropriate to aerial photography.(.ps file)*Specializations of Crossed Products*Communications in Algebra, Vol. 13, N. 12, 2003,pp.5781-5792. Determines conditions under which weakly Azumaya algebras over a field can be represented as special fibers of a homogeneous jump deformation whose general fiber is Morita equivalent to a crossed product.*Homogeneous deformations of Brauer tree algebras*, with Evelyne Zakay-Illouz.

Communications in Algebra, 31, No. 11, 2003, pp. 5243-5252,Results of the previous two papers are applied to give a natural homogeneous deformation of a Brauer tree algebra.*Folded Tilting Complexes for Brauer star algebras*, with Jeremy Rickard.

Advances in Math. 171, 2002, pp. 167-182. Shows that the tree-to-star one-sided tilting complex of Rickard and the star-to-tree one-sided tilting complex of Schaps-Zakay, when given compatible foldings, are inverse to each other. When completely folded, they give the two-term, two-sided complex of Rouquier. To appear in Advances in Mathematics.*Braid Group Action on the Refolded Tilting Complexes of the Brauer Star Algebra*, with Evelyne Zakay-Illouz.

In an earlier paper we showed that the set of "two-restricted" tilting complexes for the Brauer star algebra is in one-to-one correspondence with the set of brauer trees with an additional structure called a pointing, which determines the folding of the complex. Here we show that the subgroup of self-equivalences of the Brauer star algebra obtained by going out with one pointing and returning by another is generated by e generators which satisfy the braid relations for the Euclidean diagram which is a cycle. ps Representations of Algebras, ICRA IX (2002), pp. 434-449.*The Donald-Flanigan problem for finite reflection groups*, with M. Gerstenhaber and A. Giaquinto.

Letters in Math. Physics, 56 (2001), 41-72. Gives a global solution to the Donald-Flanigan problem for all but six of the finite reflection groups.*Pointed Brauer trees*, with Evelyne Zakay-Illouz.

Journal of Algebra, 246, 647-672 (2001). Shows that the set of "two-restricted" tilting complexes for the Brauer star algebra is in one-to-one correspondence with the set of brauer trees with an additional structure called a pointing, which determines the folding of the complex.*Combinatorial partial tilting complexes for the Brauer star algebras*, with Evelyne Zakay-Illouz.

To appear in the proceeding of the conference on rep. of algebras in Sao Paolo. Determines conditions on a complex which is a direct sum of elementary complexes with at most two indecomposable projectives which are necessary and sufficient for it to be a partial tilting comples for the Brauer star.*Quivers of blocks with normal defect group*, with Dana Shapiro and Orly Shlomo.

Proc. of Aym. in Pure Math**63**(1998). The quivers of skew products of a local algebra A by a finite p'-group are shown to be identical with the McKay graphs of certain representations of the group. This applies in particular to Brauer correspondents of blocks of finite groups. The relations are also derived from the relations of the algebra.

- Index for blocks of local subgroups
- Index for blocks of abelian defect group

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Last update: September 4, '03