Prompt heavy quarkonium production in association with a massive (anti)bottom quark at the LHC

In this work, we investigate the associated production of prompt heavy quarkonium with a massive (anti)bottom quark to leading order in the NRQCD factorization formalism at the LHC. We present numerical results for the processes involving $J/\psi,\chi_{cJ},\Upsilon$ and $\chi_{bJ}$. From our work, we find that the production rates of these processes are quite large, and these processes have the potential to be detected at the LHC. When $p_T$ is smaller than about 10 GeV, the $c\bar{c} [ ^1S_0^{(8)} ]$ state give the main contribution to the $p_T$ distribution of prompt $J/\psi$ with a (anti)bottom quark production. For the process of $pp \to \Upsilon+b(\bar{b})$, the contribution of the CSM is larger than that in the COM at low $p_T$ region. We also investigate the processes of $pp\to \chi_{cJ}+b(\bar{b})$ and $pp \to \chi_{bJ}+b(\bar{b})$, in these processes, the $p_T$ distribution are dominated by the CO Fock state contribution at the large $p_T$ region. These processes provide an interesting signature that could be studied at the LHC, and the measurement of these processes is useful to test the CSM and COM.Comment: 14 pages, 11 figures, accepted by Phys.Rev.

On the inductive blockwise Alperin weight condition for type A\mathsf A

In this paper we prove the blockwise Alperin weight conjecture for finite special linear and unitary groups, for finite groups with abelian Sylow $3$-subgroups, and verify the inductive blockwise Alperin weight condition for certain cases of groups of type $\mathsf A$. We also give a classification for the 2-blocks of special linear and unitary groups

The strengthened Brou\'{e} abelian defect group conjecture for SL(2,pn){\rm SL}(2,p^n) and GL(2,pn){\rm GL}(2,p^n)

We show that each $p$-block of ${\rm SL}(2,p^n)$ and ${\rm GL}(2,p^n)$ over an arbitrary complete discrete valuation ring is splendidly Rickard equivalent to its Brauer correspondent, hence give new evidence for a refined version of Brou\'{e}'s abelian defect group conjecture proposed by Kessar and Linckelmann

Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups

In this paper we prove that Brou\'{e}'s abelian defect group conjecture is true for the finite odd-dimensional orthogonal groups \SO_{2n+1}(q) at linear primes with $q$ odd. We first make use of the reduction theorem of Bonnaf\'{e}-Dat-Rouquier to reduce the problem to isolated blocks. Then we construct a categorical action of a Kac-Moody algebra on the category of quadratic unipotent representations of the various groups \SO_{2n+1}(q) in non-defining characteristic, by generalizing the corresponding work of Dudas-Varagnolo-Vasserot for unipotent representations. This is one of the main ingredients of our work which may be of independent interest. To obtain derived equivalences of blocks and their Brauer correspondents, we define and investigate isolated RoCK blocks. Finally, we establish the desired derived equivalence based on the work of Chuang-Rouquier that categorical actions provide derived equivalences between certain weight spaces.Comment: 120 page