The data given by Sergey Romanov is correct. I read it in the book by Gennadi Kostyrchenko "Out of the Red Shadows : Anti-Semitism in Stalin's Russia".The editing was done by G. F. Aleksandrov, Chief of Propaganda and Agitation department. The same Aleksandrov, who, together with Zueva, on 5 August 1942 wrote a 4-page note to three Secretaries of TsK, complaining that there were too many Jews in Bol'shoj theater, Moscow Conservatory and Moscow Philharmony. And also that this is partially because of the influence of Jewish music critics. "All other cathedras and conservatories ... ", wrote Aleksandrov and Zueva, " ... are in the hands of the Jews: Gol'denveizer, Fajnberg, Tsejtlin, Jampol'skij, Mostras, Dorpiak, Gedike, Pekelis et. al". That's antisemitism, pure and simple.
But Sergey fails to take into account the basic reason why Alexandrov and Zueva expressed the above sentiments.
The reason is that senior Communists knew that the privileged position of Jews in the Soviet system was one of the major reasons why that system was so unpopular with the general population. Average Russian and Ukrainian workers and peasants saw the Jews in high positions in the bureaucratic and cultural elite, and that confirmed them in their view that the whole Soviet state was a foreign tyranny exercised for the advantage of the Jews.
Therefore, those senior (non-Jewish) Communists suggested that the proportion of Jews in senior positions in Soviet society should be reduced, so as remove that particular reason for popular discontent.
The recognition that the over-representation of Jews in high places in the Bolshevik regime made it desperately unpopular with the common people goes right back to the beginnning of that regime, and even the original Jewish Bolshevik leaders were worried about it. For example, during the Civil War Trotsky suggested that there were too many Jews at headquarters and too few on the frontline, and more Jews should be sent to risk their lives at the front; he even ordered the Ukrainian Cheka, the leadership of which was 50% Jewish, to shoot some Jewish prisoners so as to disprove the claim made by anti-Bolsheviks that it was an instrument of Jewish tyranny over the Ukrainian population.