Is it permitted to learn (look in a sefer) during halel, Shema, and pesukai desimra?
I would appreciate a source. Thank you!
After you finished saying Yishtabach etc. and you are waiting for the chazan, you can learn with your eyes or think in learning (See Aruch Hashulchan 53-4, Be’er Moshe 3-20). Regarding after saying kriyas shema or between perakim of hallel I don’t know.
However while one is saying the words, of pesukei d’zimra, and instead of concentrating on what the person is saying and instead specifically putting his mind into something else, this is the personification of the pasuk (ישעיה כ”ט י”ג) “בפיו ובשפתיו כבדוני ולבי רחק ממני”. Even if the person will stop saying what he is saying and look in a sefer is incorrect, because a person should preferably not be mafsik even with other thoughts. See Piskei Teshuvos 51-8 in the name of Mekor Chaim.